diff --git a/lib/systems/inspect.nix b/lib/systems/inspect.nix
index 022e459c3945ab1..073df78797c728b 100644
--- a/lib/systems/inspect.nix
+++ b/lib/systems/inspect.nix
@@ -100,6 +100,32 @@ rec {
     ];
   };
 
+  # given two patterns, return a pattern which is their logical AND.
+  # Since a pattern is a list-of-disjuncts, this needs to
+  patternLogicalAnd = pat1_: pat2_:
+    let
+      # patterns can be either a list or a (bare) singleton; turn
+      # them into singletons for uniform handling
+      pat1 = lib.toList pat1_;
+      pat2 = lib.toList pat2_;
+    in
+      lib.concatMap (attr1:
+        map (attr2:
+          lib.recursiveUpdateUntil
+            (path: subattr1: subattr2:
+              if (builtins.intersectAttrs subattr1 subattr2) == {} || subattr1 == subattr2
+              then true
+              else throw ''
+                pattern conflict at path ${toString path}:
+                  ${builtins.toJSON subattr1}
+                  ${builtins.toJSON subattr2}
+                '')
+            attr1
+            attr2
+            )
+          pat2)
+        pat1;
+
   matchAnyAttrs = patterns:
     if builtins.isList patterns then attrs: any (pattern: matchAttrs pattern attrs) patterns
     else matchAttrs patterns;
diff --git a/pkgs/applications/networking/browsers/qutebrowser/default.nix b/pkgs/applications/networking/browsers/qutebrowser/default.nix
index 03b03724aeef19a..62bed5a34f0e640 100644
--- a/pkgs/applications/networking/browsers/qutebrowser/default.nix
+++ b/pkgs/applications/networking/browsers/qutebrowser/default.nix
@@ -12,9 +12,11 @@
 , widevine-cdm
 , enableVulkan ? stdenv.isLinux
 , vulkan-loader
+, buildPackages
 }:
 
 let
+  isQt6 = lib.versions.major qtbase.version == "6";
   pdfjs = let
     version = "3.9.179";
   in
@@ -50,10 +52,14 @@ python3.pkgs.buildPythonApplication {
   ];
 
   propagatedBuildInputs = with python3.pkgs; ([
-    pyyaml pyqt6-webengine jinja2 pygments
+    pyyaml (if isQt6 then pyqt6-webengine else pyqtwebengine) jinja2 pygments
     # scripts and userscripts libs
     tldextract beautifulsoup4
-    readability-lxml pykeepass stem
+    readability-lxml pykeepass
+  ] ++ lib.optionals ((builtins.tryEval stem.outPath).success) [
+    # error: stem-1.8.2 not supported for interpreter python3.11
+    stem
+  ] ++ [
     pynacl
     # extensive ad blocking
     adblock
@@ -80,7 +86,7 @@ python3.pkgs.buildPythonApplication {
     runHook preInstall
 
     make -f misc/Makefile \
-      PYTHON=${python3}/bin/python3 \
+      PYTHON=${buildPackages.python3}/bin/python3 \
       PREFIX=. \
       DESTDIR="$out" \
       DATAROOTDIR=/share \
diff --git a/pkgs/by-name/ja/jasper/package.nix b/pkgs/by-name/ja/jasper/package.nix
index 4e10eaa80ad83be..23171c71fbecbb1 100644
--- a/pkgs/by-name/ja/jasper/package.nix
+++ b/pkgs/by-name/ja/jasper/package.nix
@@ -48,5 +48,8 @@ stdenv.mkDerivation (finalAttrs: {
     license = lib.licenses.mit;
     maintainers = with lib.maintainers; [ AndersonTorres ];
     platforms = lib.platforms.unix;
+
+    # The value of __STDC_VERSION__ cannot be automatically determined when cross-compiling.
+    broken = stdenv.buildPlatform != stdenv.hostPlatform;
   };
 })
diff --git a/pkgs/development/libraries/qt-5/5.15/default.nix b/pkgs/development/libraries/qt-5/5.15/default.nix
index 8a859af37e9d56f..79b7ba1a79fc73f 100644
--- a/pkgs/development/libraries/qt-5/5.15/default.nix
+++ b/pkgs/development/libraries/qt-5/5.15/default.nix
@@ -11,6 +11,7 @@ Check for any minor version changes.
 , lib, stdenv, fetchurl, fetchgit, fetchpatch, fetchFromGitHub, makeSetupHook, makeWrapper
 , bison, cups ? null, harfbuzz, libGL, perl, python3
 , gstreamer, gst-plugins-base, gtk3, dconf
+, buildPackages
 , darwin
 
   # options
@@ -313,18 +314,20 @@ let
 
       qmake = callPackage ({ qtbase }: makeSetupHook {
         name = "qmake-hook";
-        propagatedBuildInputs = [ qtbase.dev ];
+        depsTargetTargetPropagated = [ qtbase.dev ];
         substitutions = {
           inherit debug;
           fix_qmake_libtool = ../hooks/fix-qmake-libtool.sh;
         };
       } ../hooks/qmake-hook.sh) { };
 
-      wrapQtAppsHook = callPackage ({ makeBinaryWrapper, qtbase, qtwayland }: makeSetupHook {
+      wrapQtAppsHook = callPackage ({ makeBinaryWrapper, qtbase, qtwayland }: makeSetupHook ({
         name = "wrap-qt5-apps-hook";
-        propagatedBuildInputs = [ qtbase.dev makeBinaryWrapper ]
+        propagatedBuildInputs = [ buildPackages.makeBinaryWrapper ];
+        depsTargetTargetPropagated = [ qtbase.dev ]
           ++ lib.optional stdenv.isLinux qtwayland.dev;
-      } ../hooks/wrap-qt-apps-hook.sh) { };
+      })
+      ../hooks/wrap-qt-apps-hook.sh) { };
     };
 
   baseScope = makeScopeWithSplicing' {
@@ -338,6 +341,12 @@ let
   });
 
   finalScope = baseScope.overrideScope(final: prev: {
-    qttranslations = bootstrapScope.qttranslations;
+    # qttranslations causes eval-time infinite recursion when
+    # cross-compiling; disabled for now.
+    qttranslations =
+      if stdenv.buildPlatform == stdenv.hostPlatform
+      then bootstrapScope.qttranslations
+      else null;
+    qutebrowser = final.callPackage ../../../../applications/networking/browsers/qutebrowser { };
   });
 in finalScope
diff --git a/pkgs/development/libraries/qt-5/hooks/qtbase-setup-hook.sh b/pkgs/development/libraries/qt-5/hooks/qtbase-setup-hook.sh
index 1b57d676e1fc5da..ccd7592dfd37efe 100644
--- a/pkgs/development/libraries/qt-5/hooks/qtbase-setup-hook.sh
+++ b/pkgs/development/libraries/qt-5/hooks/qtbase-setup-hook.sh
@@ -1,3 +1,13 @@
+if [[ "x$stdenv" != "x@qtbase_stdenv@" ]]; then
+  echo "skipping qtbase-setup-hook.sh because of mismatch:"
+  echo "  stdenv of current derivation: $stdenv"
+  echo "  stdenv of qtbase.dev dependency: @qtbase_stdenv@"
+  echo "    qtbase = @dev@"
+  return
+fi
+
+echo "running qtbase-setup-hook.sh with hostOffset=$hostOffset targetOffset=$targetOffset: @out@"
+
 if [[ -n "${__nix_qtbase-}" ]]; then
     # Throw an error if a different version of Qt was already set up.
     if [[ "$__nix_qtbase" != "@dev@" ]]; then
diff --git a/pkgs/development/libraries/qt-5/modules/qtbase.nix b/pkgs/development/libraries/qt-5/modules/qtbase.nix
index 9f0feaf94e58412..3e51ffa5792ea45 100644
--- a/pkgs/development/libraries/qt-5/modules/qtbase.nix
+++ b/pkgs/development/libraries/qt-5/modules/qtbase.nix
@@ -29,13 +29,18 @@
 , developerBuild ? false
 , decryptSslTraffic ? false
 , testers
+, buildPackages
 }:
 
 let
   debugSymbols = debug || developerBuild;
+  qtPlatformCross = plat: with plat;
+    if isLinux
+    then "linux-generic-g++"
+    else throw "Please add a qtPlatformCross entry for ${plat.config}";
 in
 
-stdenv.mkDerivation (finalAttrs: {
+stdenv.mkDerivation (finalAttrs: ({
   pname = "qtbase";
   inherit qtCompatVersion src version;
   debug = debugSymbols;
@@ -83,6 +88,13 @@ stdenv.mkDerivation (finalAttrs: {
   nativeBuildInputs = [ bison flex gperf lndir perl pkg-config which ]
     ++ lib.optionals stdenv.isDarwin [ xcbuild ];
 
+  } // lib.optionalAttrs (stdenv.buildPlatform != stdenv.hostPlatform) {
+    # `qtbase` expects to find `cc` (with no prefix) in the
+    # `$PATH`, so the following is needed even if
+    # `stdenv.buildPlatform.canExecute stdenv.hostPlatform`
+    depsBuildBuild = [ buildPackages.stdenv.cc ];
+  } // {
+
   propagatedNativeBuildInputs = [ lndir ];
 
   # libQt5Core links calls CoreFoundation APIs that call into the system ICU. Binaries linked
@@ -162,6 +174,13 @@ stdenv.mkDerivation (finalAttrs: {
     export MAKEFLAGS+=" -j$NIX_BUILD_CORES"
 
     ./bin/syncqt.pl -version $version
+  '' + lib.optionalString (!stdenv.buildPlatform.canExecute stdenv.hostPlatform) ''
+    # QT's configure script will refuse to use pkg-config unless these two environment variables are set
+    export PKG_CONFIG_SYSROOT_DIR=/
+    export PKG_CONFIG_LIBDIR=${lib.getLib pkg-config}/lib
+    echo "QMAKE_LFLAGS=''${LDFLAGS}" >> mkspecs/devices/${qtPlatformCross stdenv.hostPlatform}/qmake.conf
+    echo "QMAKE_CFLAGS=''${CFLAGS}" >> mkspecs/devices/${qtPlatformCross stdenv.hostPlatform}/qmake.conf
+    echo "QMAKE_CXXFLAGS=''${CXXFLAGS}" >> mkspecs/devices/${qtPlatformCross stdenv.hostPlatform}/qmake.conf
   '';
 
   postConfigure = ''
@@ -186,21 +205,35 @@ stdenv.mkDerivation (finalAttrs: {
     done
   '';
 
-  env.NIX_CFLAGS_COMPILE = toString ([
-    "-Wno-error=sign-compare" # freetype-2.5.4 changed signedness of some struct fields
-    ''-DNIXPKGS_QTCOMPOSE="${libX11.out}/share/X11/locale"''
-    ''-DLIBRESOLV_SO="${stdenv.cc.libc.out}/lib/libresolv"''
-    ''-DNIXPKGS_LIBXCURSOR="${libXcursor.out}/lib/libXcursor"''
-  ] ++ lib.optional libGLSupported ''-DNIXPKGS_MESA_GL="${libGL.out}/lib/libGL"''
+  env = {
+    qtbase_stdenv = stdenv.outPath;
+    NIX_CFLAGS_COMPILE = toString ([
+      "-Wno-error=sign-compare" # freetype-2.5.4 changed signedness of some struct fields
+    ] ++ lib.optionals (stdenv.buildPlatform != stdenv.hostPlatform) [
+      "-Wno-warn=free-nonheap-object"
+      "-Wno-free-nonheap-object"
+      "-w"
+    ] ++ [
+      ''-DNIXPKGS_QTCOMPOSE="${libX11.out}/share/X11/locale"''
+      ''-DLIBRESOLV_SO="${stdenv.cc.libc.out}/lib/libresolv"''
+      ''-DNIXPKGS_LIBXCURSOR="${libXcursor.out}/lib/libXcursor"''
+    ] ++ lib.optional libGLSupported ''-DNIXPKGS_MESA_GL="${libGL.out}/lib/libGL"''
     ++ lib.optional stdenv.isLinux "-DUSE_X11"
     ++ lib.optionals (stdenv.hostPlatform.system == "x86_64-darwin") [
       # ignore "is only available on macOS 10.12.2 or newer" in obj-c code
       "-Wno-error=unguarded-availability"
     ]
     ++ lib.optionals withGtk3 [
-         ''-DNIXPKGS_QGTK3_XDG_DATA_DIRS="${gtk3}/share/gsettings-schemas/${gtk3.name}"''
-         ''-DNIXPKGS_QGTK3_GIO_EXTRA_MODULES="${dconf.lib}/lib/gio/modules"''
-  ] ++ lib.optional decryptSslTraffic "-DQT_DECRYPT_SSL_TRAFFIC");
+      ''-DNIXPKGS_QGTK3_XDG_DATA_DIRS="${gtk3}/share/gsettings-schemas/${gtk3.name}"''
+      ''-DNIXPKGS_QGTK3_GIO_EXTRA_MODULES="${dconf.lib}/lib/gio/modules"''
+    ] ++ lib.optional decryptSslTraffic "-DQT_DECRYPT_SSL_TRAFFIC");
+  } // lib.optionalAttrs (stdenv.buildPlatform != stdenv.hostPlatform) {
+    NIX_CFLAGS_COMPILE_FOR_BUILD = toString ([
+      "-Wno-warn=free-nonheap-object"
+      "-Wno-free-nonheap-object"
+      "-w"
+    ]);
+  };
 
   prefixKey = "-prefix ";
 
@@ -209,6 +242,9 @@ stdenv.mkDerivation (finalAttrs: {
   # To prevent these failures, we need to override PostgreSQL detection.
   PSQL_LIBS = lib.optionalString (postgresql != null) "-L${postgresql.lib}/lib -lpq";
 
+  } // lib.optionalAttrs (stdenv.buildPlatform != stdenv.hostPlatform) {
+  configurePlatforms = [ ];
+  } // {
   # TODO Remove obsolete and useless flags once the build will be totally mastered
   configureFlags = [
     "-plugindir $(out)/$(qtPluginPrefix)"
@@ -235,11 +271,16 @@ stdenv.mkDerivation (finalAttrs: {
     "-L" "${icu.out}/lib"
     "-I" "${icu.dev}/include"
     "-pch"
+  ] ++ lib.optionals (stdenv.hostPlatform != stdenv.buildPlatform) [
+    "-device ${qtPlatformCross stdenv.hostPlatform}"
+    "-device-option CROSS_COMPILE=${stdenv.cc.targetPrefix}"
   ]
   ++ lib.optional debugSymbols "-debug"
   ++ lib.optionals developerBuild [
     "-developer-build"
     "-no-warnings-are-errors"
+  ] ++ lib.optionals (stdenv.buildPlatform != stdenv.hostPlatform) [
+    "-no-warnings-are-errors"
   ] ++ (if (!stdenv.hostPlatform.isx86_64) then [
     "-no-sse2"
   ] else [
@@ -381,4 +422,4 @@ stdenv.mkDerivation (finalAttrs: {
     platforms = platforms.unix;
   };
 
-})
+}))
diff --git a/pkgs/development/libraries/qt-5/modules/qtdeclarative.nix b/pkgs/development/libraries/qt-5/modules/qtdeclarative.nix
index 892498da43b29de..3e2136f39bcd9a1 100644
--- a/pkgs/development/libraries/qt-5/modules/qtdeclarative.nix
+++ b/pkgs/development/libraries/qt-5/modules/qtdeclarative.nix
@@ -1,4 +1,6 @@
-{ qtModule, lib, python3, qtbase, qtsvg }:
+{ lib
+, stdenv
+, qtModule, python3, qtbase, qtsvg }:
 
 qtModule {
   pname = "qtdeclarative";
@@ -21,4 +23,10 @@ qtModule {
     "bin/qmlscene"
     "bin/qmltestrunner"
   ];
+  postFixup = lib.optionalString (stdenv.buildPlatform != stdenv.hostPlatform) ''
+    mv $dev/bin/qmlformat $bin/bin/qmlformat
+    mv $dev/bin/qmltyperegistrar $bin/bin/qmltyperegistrar
+    ln -s $bin/bin/qmlformat $dev/bin/qmlformat
+    ln -s $bin/bin/qmltyperegistrar $dev/bin/qmltyperegistrar
+  '';
 }
diff --git a/pkgs/development/libraries/qt-5/modules/qtimageformats.nix b/pkgs/development/libraries/qt-5/modules/qtimageformats.nix
index f099fc6799b50f0..4775bb0b0383f6f 100644
--- a/pkgs/development/libraries/qt-5/modules/qtimageformats.nix
+++ b/pkgs/development/libraries/qt-5/modules/qtimageformats.nix
@@ -1,4 +1,6 @@
-{ qtModule
+{ lib
+, stdenv
+, qtModule
 , qtbase
 , libwebp
 , jasper
@@ -8,5 +10,11 @@
 
 qtModule {
   pname = "qtimageformats";
-  propagatedBuildInputs = [ qtbase libwebp jasper libmng libtiff ];
+  propagatedBuildInputs = [
+    qtbase libwebp
+  ] ++ lib.optionals (!jasper.meta.broken) [
+    jasper
+  ] ++ [
+    libmng libtiff
+  ];
 }
diff --git a/pkgs/development/libraries/qt-5/modules/qtwebchannel.nix b/pkgs/development/libraries/qt-5/modules/qtwebchannel.nix
index 118a5d4f96f6904..e7d6be534409e61 100644
--- a/pkgs/development/libraries/qt-5/modules/qtwebchannel.nix
+++ b/pkgs/development/libraries/qt-5/modules/qtwebchannel.nix
@@ -1,7 +1,12 @@
-{ qtModule, qtbase, qtdeclarative }:
+{ lib
+, stdenv
+, qtModule
+, qtbase
+, qtdeclarative
+}:
 
 qtModule {
   pname = "qtwebchannel";
   propagatedBuildInputs = [ qtbase qtdeclarative ];
-  outputs = [ "out" "dev" "bin" ];
+  outputs = [ "out" "dev" ] ++ lib.optionals (stdenv.hostPlatform == stdenv.buildPlatform) [ "bin" ];
 }
diff --git a/pkgs/development/libraries/qt-5/modules/qtwebengine.nix b/pkgs/development/libraries/qt-5/modules/qtwebengine.nix
index 777430af0217fc0..58f90763a2452ea 100644
--- a/pkgs/development/libraries/qt-5/modules/qtwebengine.nix
+++ b/pkgs/development/libraries/qt-5/modules/qtwebengine.nix
@@ -1,8 +1,11 @@
 { qtModule
 , qtdeclarative, qtquickcontrols, qtlocation, qtwebchannel
 
-, bison, flex, git, gperf, ninja, pkg-config, python, which
+, bison, flex, git, gperf, ninja, pkg-config, python, which, python3
 , nodejs, qtbase, perl
+, buildPackages
+, pkgsBuildTarget
+, pkgsBuildBuild
 
 , xorg, libXcursor, libXScrnSaver, libXrandr, libXtst
 , fontconfig, freetype, harfbuzz, icu, dbus, libdrm
@@ -27,12 +30,45 @@
 , pipewireSupport ? stdenv.isLinux
 , pipewire_0_2
 , postPatch ? ""
+, nspr
+, lndir
+, dbusSupport ? !stdenv.isDarwin, expat
 }:
 
-qtModule {
+let
+  # qtwebengine expects to find an executable in $PATH which runs on
+  # the build platform yet knows about the host `.pc` files.  Most
+  # configury allows setting $PKG_CONFIG to point to an
+  # arbitrarily-named script which serves this purpose; however QT
+  # insists that it is named `pkg-config` with no target prefix.  So
+  # we re-wrap the host platform's pkg-config.
+  pkg-config-wrapped-without-prefix = stdenv.mkDerivation {
+    name = "pkg-config-wrapper-without-target-prefix";
+    dontUnpack = true;
+    dontBuild = true;
+    installPhase = ''
+      mkdir -p $out/bin
+      ln -s '${buildPackages.pkg-config}/bin/${buildPackages.pkg-config.targetPrefix}pkg-config' $out/bin/pkg-config
+    '';
+  };
+
+  qtPlatformCross = plat: with plat;
+    if isLinux
+    then "linux-generic-g++"
+    else throw "Please add a qtPlatformCross entry for ${plat.config}";
+
+in
+
+qtModule ({
   pname = "qtwebengine";
   nativeBuildInputs = [
     bison flex git gperf ninja pkg-config python which gn nodejs
+  ] ++ lib.optionals (stdenv.buildPlatform != stdenv.hostPlatform) [
+    perl
+    lndir (lib.getDev pkgsBuildTarget.targetPackages.qt5.qtbase)
+    pkgsBuildBuild.pkg-config
+    (lib.getDev pkgsBuildTarget.targetPackages.qt5.qtquickcontrols)
+    pkg-config-wrapped-without-prefix
   ] ++ lib.optional stdenv.isDarwin xcbuild;
   doCheck = true;
   outputs = [ "bin" "dev" "out" ];
@@ -108,16 +144,25 @@ qtModule {
       --replace "-Wl,-fatal_warnings" ""
   '') + postPatch;
 
-  env.NIX_CFLAGS_COMPILE = toString (lib.optionals stdenv.cc.isGNU [
-    # with gcc8, -Wclass-memaccess became part of -Wall and this exceeds the logging limit
-    "-Wno-class-memaccess"
-  ] ++ lib.optionals (stdenv.hostPlatform.gcc.arch or "" == "sandybridge") [
-    # it fails when compiled with -march=sandybridge https://github.com/NixOS/nixpkgs/pull/59148#discussion_r276696940
-    # TODO: investigate and fix properly
-    "-march=westmere"
-  ] ++ lib.optionals stdenv.cc.isClang [
-    "-Wno-elaborated-enum-base"
-  ]);
+  env = {
+    NIX_CFLAGS_COMPILE =
+      toString (
+        lib.optionals (stdenv.buildPlatform != stdenv.hostPlatform) [
+          "-w "
+        ] ++ lib.optionals stdenv.cc.isGNU [
+          # with gcc8, -Wclass-memaccess became part of -Wall and this exceeds the logging limit
+          "-Wno-class-memaccess"
+        ] ++ lib.optionals (stdenv.hostPlatform.gcc.arch or "" == "sandybridge") [
+          # it fails when compiled with -march=sandybridge https://github.com/NixOS/nixpkgs/pull/59148#discussion_r276696940
+          # TODO: investigate and fix properly
+          "-march=westmere"
+        ] ++ lib.optionals stdenv.cc.isClang [
+          "-Wno-elaborated-enum-base"
+        ]);
+  } // lib.optionalAttrs (stdenv.buildPlatform != stdenv.hostPlatform) {
+    NIX_CFLAGS_LINK = "-Wl,--no-warn-search-mismatch";
+    "NIX_CFLAGS_LINK_${buildPackages.stdenv.cc.suffixSalt}" = "-Wl,--no-warn-search-mismatch";
+  };
 
   preConfigure = ''
     export NINJAFLAGS=-j$NIX_BUILD_CORES
@@ -125,10 +170,15 @@ qtModule {
     if [ -d "$PWD/tools/qmake" ]; then
         QMAKEPATH="$PWD/tools/qmake''${QMAKEPATH:+:}$QMAKEPATH"
     fi
+  '' + lib.optionalString (stdenv.hostPlatform != stdenv.buildPlatform) ''
+    export QMAKE_CC=$CC
+    export QMAKE_CXX=$CXX
+    export QMAKE_LINK=$CXX
+    export QMAKE_AR=$AR
   '';
 
   qmakeFlags = [ "--" "-system-ffmpeg" ]
-    ++ lib.optional pipewireSupport "-webengine-webrtc-pipewire"
+    ++ lib.optional (pipewireSupport && stdenv.buildPlatform == stdenv.hostPlatform) "-webengine-webrtc-pipewire"
     ++ lib.optional enableProprietaryCodecs "-proprietary-codecs";
 
   propagatedBuildInputs = [
@@ -226,7 +276,9 @@ qtModule {
   dontUseNinjaBuild = true;
   dontUseNinjaInstall = true;
 
-  postInstall = lib.optionalString stdenv.isLinux ''
+  postInstall = lib.optionalString (stdenv.buildPlatform != stdenv.hostPlatform) ''
+    mkdir -p $out/libexec
+  '' + lib.optionalString stdenv.isLinux ''
     cat > $out/libexec/qt.conf <<EOF
     [Paths]
     Prefix = ..
@@ -245,21 +297,32 @@ qtModule {
 
     # qtwebengine-5.15.8: "QtWebEngine can only be built for x86,
     # x86-64, ARM, Aarch64, and MIPSel architectures."
-    platforms =
-      lib.trivial.pipe lib.systems.doubles.all [
-        (map (double: lib.systems.elaborate { system = double; }))
-        (lib.lists.filter (parsedPlatform: with parsedPlatform;
-          isUnix &&
-          (isx86_32  ||
-           isx86_64  ||
-           isAarch32 ||
-           isAarch64 ||
-           (isMips && isLittleEndian))))
-        (map (plat: plat.system))
-      ];
+    platforms = with lib.systems.inspect.patterns;
+      let inherit (lib.systems.inspect) patternLogicalAnd;
+      in concatMap (patternLogicalAnd isUnix) (lib.concatMap lib.toList [
+        isx86_32
+        isx86_64
+        isAarch32
+        isAarch64
+        (patternLogicalAnd isMips isLittleEndian)
+      ]);
     broken = stdenv.isDarwin && stdenv.isx86_64;
 
     # This build takes a long time; particularly on slow architectures
     timeout = 24 * 3600;
   };
-}
+
+} // lib.optionalAttrs (stdenv.buildPlatform != stdenv.hostPlatform) {
+  configurePlatforms = [ ];
+  # to get progress output in `nix-build` and `nix build -L`
+  preBuild = ''
+    export TERM=dumb
+  '';
+  depsBuildBuild = [
+    pkgsBuildBuild.stdenv
+    zlib
+    nss
+    nspr
+  ];
+
+})
diff --git a/pkgs/development/libraries/qt-5/qtModule.nix b/pkgs/development/libraries/qt-5/qtModule.nix
index 7d73e652b6ffb39..54d24e46092f283 100644
--- a/pkgs/development/libraries/qt-5/qtModule.nix
+++ b/pkgs/development/libraries/qt-5/qtModule.nix
@@ -1,4 +1,13 @@
-{ lib, mkDerivation, perl, qmake, patches, srcs }:
+{ lib
+, stdenv
+, buildPackages
+, mkDerivation
+, perl
+, qmake
+, patches
+, srcs
+, pkgsHostTarget
+}:
 
 let inherit (lib) licenses maintainers platforms; in
 
@@ -14,10 +23,18 @@ mkDerivation (args // {
   inherit pname version src;
   patches = (args.patches or []) ++ (patches.${pname} or []);
 
-  nativeBuildInputs = (args.nativeBuildInputs or []) ++ [ perl qmake ];
+  nativeBuildInputs =
+    (args.nativeBuildInputs or []) ++ [
+      perl qmake
+    ] ++ lib.optionals (stdenv.buildPlatform != stdenv.hostPlatform) [
+      pkgsHostTarget.qt5.qtbase.dev
+    ];
   propagatedBuildInputs =
     (lib.warnIf (args ? qtInputs) "qt5.qtModule's qtInputs argument is deprecated" args.qtInputs or []) ++
     (args.propagatedBuildInputs or []);
+} // lib.optionalAttrs (stdenv.buildPlatform != stdenv.hostPlatform) {
+  depsBuildBuild = [ buildPackages.stdenv.cc ] ++ (args.depsBuildBuild or []);
+} // {
 
   outputs = args.outputs or [ "out" "dev" ];
   setOutputFlags = args.setOutputFlags or false;
diff --git a/pkgs/development/python-modules/pyqt/5.x.nix b/pkgs/development/python-modules/pyqt/5.x.nix
index 12d2ea182af0290..c514b9f8358437d 100644
--- a/pkgs/development/python-modules/pyqt/5.x.nix
+++ b/pkgs/development/python-modules/pyqt/5.x.nix
@@ -12,6 +12,7 @@
 , pyqt5_sip
 , pyqt-builder
 , libsForQt5
+, enableVerbose ? true
 , withConnectivity ? false
 , withMultimedia ? false
 , withWebKit ? false
@@ -19,6 +20,9 @@
 , withLocation ? false
 , withSerialPort ? false
 , withTools ? false
+, pkgsBuildTarget
+, buildPackages
+, dbusSupport ? !stdenv.isDarwin
 }:
 
 buildPythonPackage rec {
@@ -45,6 +49,7 @@ buildPythonPackage rec {
   # be more verbose
   ''
     cat >> pyproject.toml <<EOF
+  '' + lib.optionalString enableVerbose ''
     [tool.sip.project]
     verbose = true
   ''
@@ -55,6 +60,37 @@ buildPythonPackage rec {
     minimum-macos-version = "11.0"
   '' + ''
     EOF
+  ''
+
+  # pyqt-builder tries to compile *and run* these programs.  This
+  # is really sad because the only thing they do is print out a
+  # flag based on whether or not some compile-time symbol was
+  # defined.  This could all be done without having to *execute*
+  # cross-compiled programs!
+  #
+  # Here is the complete list of things checked:
+  #
+  # QT_NO_PRINTDIALOG                                                           => PyQt_PrintDialog
+  # QT_NO_PRINTER                                                               => PyQt_Printer
+  # QT_NO_PRINTPREVIEWDIALOG                                                    => PyQt_PrintPreviewDialog
+  # QT_NO_PRINTPREVIEWWIDGET                                                    => PyQt_PrintPreviewWidget
+  # QT_NO_SSL                                                                   => PyQt_SSL
+  # QT_SHARED || QT_DLL                                                         => shared (otherwise static)
+  # QT_NO_PROCESS                                                               => PyQt_Process
+  # QT_NO_FPU || Q_PROCESSOR_ARM || Q_OS_WINCE                                  => PyQt_qreal_double
+  # sizeof (qreal) != sizeof (double)                                           => PyQt_qreal_double
+  # !Q_COMPILER_CONSTEXPR !Q_COMPILER_UNIFORM_INIT                              => PyQt_CONSTEXPR
+  # QT_NO_ACCESSIBILITY                                                         => PyQt_Accessibility
+  # QT_NO_OPENGL                                                                => PyQt_OpenGL PyQt_Desktop_OpenGL
+  # defined(QT_OPENGL_ES) || defined(QT_OPENGL_ES_2) || defined(QT_OPENGL_ES_3) => PyQt_Desktop_OpenGL
+  # QT_NO_RAWFONT                                                               => PyQt_RawFont
+  # QT_NO_SESSIONMANAGER                                                        => PyQt_SessionManager
+  #
+  + lib.optionalString (!(stdenv.buildPlatform.canExecute stdenv.hostPlatform)) ''
+    rm config-tests/cfgtest_QtCore.cpp
+    rm config-tests/cfgtest_QtGui.cpp
+    rm config-tests/cfgtest_QtNetwork.cpp
+    rm config-tests/cfgtest_QtPrintSupport.cpp
   '';
 
   enableParallelBuilding = true;
@@ -68,16 +104,27 @@ buildPythonPackage rec {
     export MAKEFLAGS+="''${enableParallelBuilding:+-j$NIX_BUILD_CORES}"
   '';
 
+  # tons of warnings from subpackages, no point in playing whack-a-mole
+  env = lib.optionalAttrs (!enableVerbose) {
+    NIX_CFLAGS_COMPILE = "-w";
+  };
+
   outputs = [ "out" "dev" ];
 
   dontWrapQtApps = true;
 
-  nativeBuildInputs = with libsForQt5; [
+  nativeBuildInputs = [
     pkg-config
-    qmake
+  ] ++ lib.optionals (stdenv.buildPlatform == stdenv.hostPlatform) [
+    libsForQt5.qmake
+  ] ++ [
     setuptools
     lndir
     sip
+  ] ++ (with pkgsBuildTarget.targetPackages.libsForQt5; [
+  ] ++ lib.optionals (stdenv.buildPlatform != stdenv.hostPlatform) [
+    qmake
+  ] ++ [
     qtbase
     qtsvg
     qtdeclarative
@@ -90,11 +137,13 @@ buildPythonPackage rec {
     ++ lib.optional withLocation qtlocation
     ++ lib.optional withSerialPort qtserialport
     ++ lib.optional withTools qttools
-  ;
+  );
 
   buildInputs = with libsForQt5; [
     dbus
+  ] ++ lib.optionals (stdenv.buildPlatform == stdenv.hostPlatform) [
     qtbase
+  ] ++ [
     qtsvg
     qtdeclarative
     pyqt-builder
diff --git a/pkgs/development/python-modules/pyqtwebengine/default.nix b/pkgs/development/python-modules/pyqtwebengine/default.nix
index 7ad39633b7e51e5..71abe839a7893e1 100644
--- a/pkgs/development/python-modules/pyqtwebengine/default.nix
+++ b/pkgs/development/python-modules/pyqtwebengine/default.nix
@@ -1,13 +1,14 @@
 { lib, stdenv, pythonPackages, fetchPypi, pkg-config
-, qmake, qtbase, qtsvg, qtwebengine
+, qmake, qtbase, qtsvg, qtwebengine, qtwebchannel, qtdeclarative
 , wrapQtAppsHook
 , darwin
+, buildPackages
 }:
 
 let
   inherit (pythonPackages) buildPythonPackage python isPy27 pyqt5 sip pyqt-builder;
   inherit (darwin) autoSignDarwinBinariesHook;
-in buildPythonPackage rec {
+in buildPythonPackage (rec {
   pname = "PyQtWebEngine";
   version = "5.15.4";
   format = "pyproject";
@@ -29,12 +30,18 @@ in buildPythonPackage rec {
   nativeBuildInputs = [
     pkg-config
     qmake
+  ] ++ lib.optionals (stdenv.buildPlatform == stdenv.hostPlatform) [
     sip
+  ] ++ lib.optionals (stdenv.buildPlatform != stdenv.hostPlatform) [
+    buildPackages.python3Packages.sip
+  ] ++ [
     qtbase
     qtsvg
     qtwebengine
     pyqt-builder
     pythonPackages.setuptools
+  ] ++ lib.optionals (stdenv.buildPlatform != stdenv.hostPlatform) [
+    qtdeclarative
   ] ++ lib.optionals (stdenv.isDarwin && stdenv.isAarch64) [
     autoSignDarwinBinariesHook
   ];
@@ -44,6 +51,9 @@ in buildPythonPackage rec {
     qtbase
     qtsvg
     qtwebengine
+  ] ++ lib.optionals (stdenv.buildPlatform != stdenv.hostPlatform) [
+    qtwebchannel
+    qtdeclarative
   ];
 
   propagatedBuildInputs = [ pyqt5 ];
@@ -71,6 +81,13 @@ in buildPythonPackage rec {
     description = "Python bindings for Qt5";
     homepage    = "http://www.riverbankcomputing.co.uk";
     license     = licenses.gpl3;
-    platforms   = lib.lists.intersectLists qtwebengine.meta.platforms platforms.mesaPlatforms;
+    hydraPlatforms = lib.lists.intersectLists qtwebengine.meta.platforms platforms.mesaPlatforms;
   };
-}
+} // lib.optionalAttrs (stdenv.buildPlatform != stdenv.hostPlatform) {
+  # TODO: figure out why the env hooks aren't adding these inclusions automatically
+  env.NIX_CFLAGS_COMPILE =
+    lib.concatStringsSep " " [
+      "-I${lib.getDev qtbase}/include/QtPrintSupport/"
+      "-I${lib.getDev qtwebchannel}/include/QtWebChannel/"
+    ];
+})
diff --git a/pkgs/test/cross/default.nix b/pkgs/test/cross/default.nix
index f844fc2b8ec5547..9f8209de17ed294 100644
--- a/pkgs/test/cross/default.nix
+++ b/pkgs/test/cross/default.nix
@@ -151,6 +151,10 @@ let
     # lots of interesting corner cases.  Only expected to work for
     # x86_64-linux buildPlatform.
     pkgs.pkgsMusl.pkgsCross.gnu64.hello
+
+    # Two web browsers -- exercises almost the entire packageset
+    pkgs.pkgsCross.aarch64-multiplatform.qt5.qutebrowser
+    pkgs.pkgsCross.aarch64-multiplatform.firefox
   ];
 
 in {
diff --git a/pkgs/top-level/all-packages.nix b/pkgs/top-level/all-packages.nix
index af609d1e8a3ad6b..6d88b572739b737 100644
--- a/pkgs/top-level/all-packages.nix
+++ b/pkgs/top-level/all-packages.nix
@@ -24670,6 +24670,7 @@ with pkgs;
       inherit (__splicedPackages)
         makeScopeWithSplicing' generateSplicesForMkScope lib fetchurl fetchpatch fetchgit fetchFromGitHub makeSetupHook makeWrapper
         bison cups dconf harfbuzz libGL perl gtk3 python3
+        buildPackages
         darwin;
       inherit (__splicedPackages.gst_all_1) gstreamer gst-plugins-base;
       inherit config;