diff --git a/NEWS.md b/NEWS.md
index 5fd6406725e68..9edc8836abf79 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -84,6 +84,10 @@ This section lists changes that do not have deprecation warnings.
   * In macro calls with parentheses, e.g. `@m(a=1)`, assignments are now parsed as
     `=` expressions, instead of as `kw` expressions. ([#7669])
 
+  * (µ "micro" and ɛ "latin epsilon") are considered equivalent to
+    the corresponding Greek characters in identifiers.  `\varepsilon`
+    now tab-completes to U+03B5 (greek small letter epsilon) ([#19464]).
+
 Library improvements
 --------------------
 
diff --git a/base/latex_symbols.jl b/base/latex_symbols.jl
index ffa122464446e..2e2d2af8da657 100644
--- a/base/latex_symbols.jl
+++ b/base/latex_symbols.jl
@@ -257,7 +257,7 @@ const latex_symbols = Dict(
     "\\Elzopeno" => "ɔ",
     "\\Elzrtld" => "ɖ",
     "\\Elzschwa" => "ə",
-    "\\varepsilon" => "ɛ",
+    "\\varepsilon" => "ε",
     "\\Elzpgamma" => "ɣ",
     "\\Elzpbgam" => "ɤ",
     "\\Elztrnh" => "ɥ",
diff --git a/deps/checksums/utf8proc-40e605959eb5cb90b2587fa88e3b661558fbc55a.tar.gz/md5 b/deps/checksums/utf8proc-40e605959eb5cb90b2587fa88e3b661558fbc55a.tar.gz/md5
new file mode 100644
index 0000000000000..0a257a0c03698
--- /dev/null
+++ b/deps/checksums/utf8proc-40e605959eb5cb90b2587fa88e3b661558fbc55a.tar.gz/md5
@@ -0,0 +1 @@
+f33af304538c3afba3b1d0ebae8e4555
diff --git a/deps/checksums/utf8proc-40e605959eb5cb90b2587fa88e3b661558fbc55a.tar.gz/sha512 b/deps/checksums/utf8proc-40e605959eb5cb90b2587fa88e3b661558fbc55a.tar.gz/sha512
new file mode 100644
index 0000000000000..7fb13653ee1fa
--- /dev/null
+++ b/deps/checksums/utf8proc-40e605959eb5cb90b2587fa88e3b661558fbc55a.tar.gz/sha512
@@ -0,0 +1 @@
+17a2df079e726a4ae1f10fcf48a7a771c2bcc93c7938f88148e1aa3b6cf9d250eb33cd7a9d8de54f29360e71c71e59b77996ba28dd894676888dc0453d67e9bb
diff --git a/deps/checksums/utf8proc-e3a5ed7b8bb5d0c6bb313d3e1f4d072c04113c4b.tar.gz/md5 b/deps/checksums/utf8proc-e3a5ed7b8bb5d0c6bb313d3e1f4d072c04113c4b.tar.gz/md5
deleted file mode 100644
index 2b394ed2436f8..0000000000000
--- a/deps/checksums/utf8proc-e3a5ed7b8bb5d0c6bb313d3e1f4d072c04113c4b.tar.gz/md5
+++ /dev/null
@@ -1 +0,0 @@
-c85e1275fb558d9bad5c3fa0b496e457
diff --git a/deps/checksums/utf8proc-e3a5ed7b8bb5d0c6bb313d3e1f4d072c04113c4b.tar.gz/sha512 b/deps/checksums/utf8proc-e3a5ed7b8bb5d0c6bb313d3e1f4d072c04113c4b.tar.gz/sha512
deleted file mode 100644
index 08976e711026b..0000000000000
--- a/deps/checksums/utf8proc-e3a5ed7b8bb5d0c6bb313d3e1f4d072c04113c4b.tar.gz/sha512
+++ /dev/null
@@ -1 +0,0 @@
-e7dd0a575f94621c7b56eca28fced5934c3dd6675877842287d04ad74bacaf446d8e8c8cdce14963c819b09786037c0c46679ff2dc42818497bb1acbbb9751e6
diff --git a/deps/utf8proc.version b/deps/utf8proc.version
index ab5f84a39687f..cf8cc7de8f10c 100644
--- a/deps/utf8proc.version
+++ b/deps/utf8proc.version
@@ -1,2 +1,2 @@
-UTF8PROC_BRANCH=v2.0.2
-UTF8PROC_SHA1=e3a5ed7b8bb5d0c6bb313d3e1f4d072c04113c4b
+UTF8PROC_BRANCH=v2.1
+UTF8PROC_SHA1=40e605959eb5cb90b2587fa88e3b661558fbc55a
diff --git a/doc/src/manual/variables.md b/doc/src/manual/variables.md
index 087f4d98d5473..e834150771a86 100644
--- a/doc/src/manual/variables.md
+++ b/doc/src/manual/variables.md
@@ -108,6 +108,13 @@ ERROR: syntax: unexpected "="
  ...
 ```
 
+Some Unicode characters are considered to be equivalent in identifiers.
+Different ways of entering Unicode combining characters (e.g., accents)
+are treated as equivalent (specifically, Julia identifiers are NFC-normalized).
+The Unicode characters `ɛ` (U+025B: Latin small letter open e)
+and `µ` (U+00B5: micro sign) are treated as equivalent to the corresponding
+Greek letters, because the former are easily accessible via some input methods.
+
 ## Stylistic Conventions
 
 While Julia imposes few restrictions on valid names, it has become useful to adopt the following
diff --git a/src/flisp/flisp.c b/src/flisp/flisp.c
index 6b485d0362428..bc3b2e93137a4 100644
--- a/src/flisp/flisp.c
+++ b/src/flisp/flisp.c
@@ -2305,6 +2305,7 @@ static const builtinspec_t core_builtin_info[] = {
 
 extern void builtins_init(fl_context_t *fl_ctx);
 extern void comparehash_init(fl_context_t *fl_ctx);
+extern void jl_charmap_init(fl_context_t *fl_ctx);
 
 static void lisp_init(fl_context_t *fl_ctx, size_t initial_heapsize)
 {
@@ -2337,6 +2338,7 @@ static void lisp_init(fl_context_t *fl_ctx, size_t initial_heapsize)
     fl_ctx->consflags = bitvector_new(fl_ctx->heapsize/sizeof(cons_t), 1);
     fl_print_init(fl_ctx);
     comparehash_init(fl_ctx);
+    jl_charmap_init(fl_ctx);
     fl_ctx->N_STACK = 262144;
     fl_ctx->Stack = (value_t*)malloc(fl_ctx->N_STACK*sizeof(value_t));
     CHECK_ALIGN8(fl_ctx->Stack);
diff --git a/src/flisp/flisp.h b/src/flisp/flisp.h
index fea46e570ea5e..c661d7a319205 100644
--- a/src/flisp/flisp.h
+++ b/src/flisp/flisp.h
@@ -389,6 +389,7 @@ struct _fl_context_t {
     fltype_t *builtintype;
 
     htable_t equal_eq_hashtable;
+    htable_t jl_charmap;
 
     value_t tablesym;
     fltype_t *tabletype;
diff --git a/src/flisp/julia_charmap.h b/src/flisp/julia_charmap.h
new file mode 100644
index 0000000000000..bed88a9ace4cd
--- /dev/null
+++ b/src/flisp/julia_charmap.h
@@ -0,0 +1,7 @@
+/* Array of {original codepoint, replacement codepoint} normalizations
+   to perform on Julia identifiers, to canonicalize characters that
+   are both easily confused and easily inputted by accident. */
+static const uint32_t charmap[][2] = {
+    { 0x025B, 0x03B5 }, // latin small letter open e -> greek small letter epsilon
+    { 0x00B5, 0x03BC }, // micro sign -> greek small letter mu
+};
diff --git a/src/flisp/julia_extensions.c b/src/flisp/julia_extensions.c
index f43fbd7479ec2..32aa5cab31d80 100644
--- a/src/flisp/julia_extensions.c
+++ b/src/flisp/julia_extensions.c
@@ -152,14 +152,46 @@ value_t fl_julia_identifier_start_char(fl_context_t *fl_ctx, value_t *args, uint
     return jl_id_start_char(wc) ? fl_ctx->T : fl_ctx->F;
 }
 
-// return NFC-normalized UTF8-encoded version of s
+#include "julia_charmap.h"
+#define _equal_wchar_(x, y, ctx) ((x) == (y))
+#define _hash_wchar_(x, ctx) inthash((uint32_t) ((uintptr_t) (x)))
+#include "htable.inc"
+HTIMPL_R(wcharhash, _hash_wchar_, _equal_wchar_)
+
+void jl_charmap_init(fl_context_t *fl_ctx)
+{
+    size_t charmap_len = sizeof(charmap) / (2*sizeof(uint32_t));
+    size_t i;
+    htable_t *h = htable_new(&fl_ctx->jl_charmap, charmap_len);
+    assert(sizeof(uint32_t) <= sizeof(void*));
+    for (i = 0; i < charmap_len; ++i) {
+        /* Store charmap in a hash table.  Typecasting codepoints
+           directly to pointer keys works because pointers are at
+           least 32 bits on all Julia-supported systems, and because
+           we never map anything to U+0001 (since HT_NOTFOUND is (void*)1). */
+        assert((void*)charmap[i][1] != HT_NOTFOUND);
+        wcharhash_put_r(h, (void*)((uintptr_t)charmap[i][0]),
+                           (void*)((uintptr_t)charmap[i][1]), (void*)fl_ctx);
+    }
+}
+utf8proc_int32_t jl_charmap_map(utf8proc_int32_t c, void *fl_ctx_)
+{
+    fl_context_t *fl_ctx = (fl_context_t *) fl_ctx_;
+    htable_t *h = &fl_ctx->jl_charmap;
+    void *v = wcharhash_get_r(h, (void*)((uintptr_t)c), (void*) fl_ctx);
+    return v == HT_NOTFOUND ? c : (utf8proc_int32_t) ((uintptr_t) v);
+}
+
+// return NFC-normalized UTF8-encoded version of s, with
+// additional custom normalizations defined by jl_charmap above.
 static char *normalize(fl_context_t *fl_ctx, char *s)
 {
     // options equivalent to utf8proc_NFC:
     const int options = UTF8PROC_NULLTERM|UTF8PROC_STABLE|UTF8PROC_COMPOSE;
     ssize_t result;
     size_t newlen;
-    result = utf8proc_decompose((uint8_t*) s, 0, NULL, 0, (utf8proc_option_t)options);
+    result = utf8proc_decompose_custom((uint8_t*) s, 0, NULL, 0, (utf8proc_option_t)options,
+                                       jl_charmap_map, (void*) fl_ctx);
     if (result < 0) goto error;
     newlen = result * sizeof(int32_t) + 1;
     if (newlen > fl_ctx->jlbuflen) {
@@ -167,7 +199,8 @@ static char *normalize(fl_context_t *fl_ctx, char *s)
         fl_ctx->jlbuf = realloc(fl_ctx->jlbuf, fl_ctx->jlbuflen);
         if (!fl_ctx->jlbuf) lerror(fl_ctx, fl_ctx->OutOfMemoryError, "error allocating UTF8 buffer");
     }
-    result = utf8proc_decompose((uint8_t*)s,0, (int32_t*)fl_ctx->jlbuf,result, (utf8proc_option_t)options);
+    result = utf8proc_decompose_custom((uint8_t*)s,0, (int32_t*)fl_ctx->jlbuf,result, (utf8proc_option_t)options,
+                                       jl_charmap_map, (void*) fl_ctx);
     if (result < 0) goto error;
     result = utf8proc_reencode((int32_t*)fl_ctx->jlbuf,result, (utf8proc_option_t)options);
     if (result < 0) goto error;
diff --git a/test/parse.jl b/test/parse.jl
index a73eb5de957c2..eb3ac9f351849 100644
--- a/test/parse.jl
+++ b/test/parse.jl
@@ -888,6 +888,19 @@ let f = function (x; kw...)
     @test g(1) == (1, 2)
 end
 
+# normalization of Unicode symbols (#19464)
+let ε=1, μ=2, x=3, î=4
+    # issue #5434 (mu vs micro):
+    @test parse("\u00b5") === parse("\u03bc")
+    @test µ == μ == 2
+    # NFC normalization of identifiers:
+    @test parse("\u0069\u0302") === parse("\u00ee")
+    @test î == 4
+    # latin vs greek ε (#14751)
+    @test parse("\u025B") === parse("\u03B5")
+    @test ɛ == ε == 1
+end
+
 # issue #8925
 let
     global const (c8925, d8925) = (3, 4)