diff --git a/CHANGES.rst b/CHANGES.rst
index e2144f3fd8..7d46055b77 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -6,6 +6,8 @@ New Features
 
 - Snackbar queue priority and history access. [#1352]
 
+- Subset Tools plugin now shows information for composite subsets. [#1378]
+
 - Plot options are simplified and include an advanced mode to act on multiple viewers/layers
   simultaneously. [#1343]
 
diff --git a/docs/specviz/plugins.rst b/docs/specviz/plugins.rst
index 10c7c96e80..d54fbace9f 100644
--- a/docs/specviz/plugins.rst
+++ b/docs/specviz/plugins.rst
@@ -61,8 +61,9 @@ applied by the selector tool. Note that these are synched with the subset tools
 in the app-level toolbar.
 
 If an existing subset is selected, the parameters of the subset will also be 
-shown. Note that parameters compound regions (e.g., a subset with three disjoint 
-regions) are not currently displayed.
+shown. Note that while parameters for compound regions (e.g., a subset with 
+three disjoint regions) are displayed, the logical operations joining them
+(``OR``, ``AND``, etc.) are not.
 
 .. _gaussian-smooth:
 
diff --git a/jdaviz/configs/default/plugins/subset_plugin/subset_plugin.py b/jdaviz/configs/default/plugins/subset_plugin/subset_plugin.py
index 902002df9e..5644589d8f 100644
--- a/jdaviz/configs/default/plugins/subset_plugin/subset_plugin.py
+++ b/jdaviz/configs/default/plugins/subset_plugin/subset_plugin.py
@@ -1,10 +1,9 @@
 from glue.core.message import EditSubsetMessage, SubsetUpdateMessage
 from glue.core.edit_subset_mode import (AndMode, AndNotMode, OrMode,
                                         ReplaceMode, XorMode)
-from glue.core.subset import (RoiSubsetState, RangeSubsetState,
-                              OrState, AndState, XorState, InvertState)
+from glue.core.subset import RoiSubsetState, RangeSubsetState, CompositeSubsetState
 from glue_jupyter.widgets.subset_mode_vuetify import SelectionModeMenu
-from traitlets import List, Unicode, Bool, Dict, observe
+from traitlets import List, Unicode, Bool, observe
 
 from jdaviz.core.registries import tray_registry
 from jdaviz.core.template_mixin import TemplateMixin, SubsetSelect
@@ -27,9 +26,9 @@ class SubsetPlugin(TemplateMixin):
     subset_items = List([]).tag(sync=True)
     subset_selected = Unicode("Create new").tag(sync=True)
     mode_selected = Unicode('add').tag(sync=True)
-    show_region_info = Bool(False).tag(sync=True)
-    subset_classname = Unicode('').tag(sync=True)
-    subset_definition = Dict({}).tag(sync=True)
+    show_region_info = Bool(True).tag(sync=True)
+    subset_types = List([]).tag(sync=True)
+    subset_definitions = List([]).tag(sync=True)
     has_subset_details = Bool(False).tag(sync=True)
 
     def __init__(self, *args, **kwargs):
@@ -67,7 +66,7 @@ def _sync_selected_from_state(self, *args):
 
     def _on_subset_update(self, *args):
         self._sync_selected_from_state(*args)
-        self._get_region_definition(*args)
+        self._get_subset_definition(*args)
         subset_to_update = self.session.edit_subset_mode.edit_subset[0]
         self.subset_select._update_subset(subset_to_update, attribute="type")
 
@@ -86,7 +85,7 @@ def _sync_selected_from_ui(self, change):
             return
 
         if change['new'] != self.subset_select.default_text:
-            self._get_region_definition(change['new'])
+            self._get_subset_definition(change['new'])
         self.show_region_info = change['new'] != self.subset_select.default_text
         m = [s for s in self.app.data_collection.subset_groups if s.label == change['new']]
         if m != self.session.edit_subset_mode.edit_subset:
@@ -101,40 +100,65 @@ def _mode_selected_changed(self, event={}):
             self.session.edit_subset_mode = self.mode_selected
     '''
 
-    def _get_region_definition(self, *args):
-        self.subset_definition = {}
+    def _unpack_nested_subset(self, subset_state):
+        '''
+        Navigate through the tree of subset states for composite
+        subsets made up of multiple regions.
+        '''
+        if isinstance(subset_state, CompositeSubsetState):
+            self._unpack_nested_subset(subset_state.state1)
+            self._unpack_nested_subset(subset_state.state2)
+        else:
+            if subset_state is not None:
+                self._get_subset_subregion_definition(subset_state)
+
+    def _get_subset_subregion_definition(self, subset_state):
+        """
+        Get the type and parameters for a single region in the subset. Note that
+        the string type and operation (if in a composite subset) need to be stored
+        separately from the float parameters for display reasons.
+        """
+        subset_type = {}
+        subset_definition = None
+
+        if isinstance(subset_state, RoiSubsetState):
+            subset_classname = subset_state.roi.__class__.__name__
+            if subset_classname == "CircularROI":
+                x, y = subset_state.roi.get_center()
+                subset_definition = {"X Center": x,
+                                     "Y Center": y,
+                                     "Radius": subset_state.roi.radius}
+
+            elif subset_classname == "RectangularROI":
+                subset_definition = {}
+                for att in ("Xmin", "Xmax", "Ymin", "Ymax"):
+                    subset_definition[att] = getattr(subset_state.roi, att.lower())
+
+            elif subset_classname == "EllipticalROI":
+                subset_definition = {"X Center": subset_state.roi.xc,
+                                     "Y Center": subset_state.roi.yc,
+                                     "X Radius": subset_state.roi.radius_x,
+                                     "Y Radius": subset_state.roi.radius_y}
+            subset_type["Subset type"] = subset_classname
+
+        elif isinstance(subset_state, RangeSubsetState):
+            subset_definition = {"Upper bound": subset_state.hi,
+                                 "Lower bound": subset_state.lo}
+            subset_type["Subset type"] = "Range"
+
+        if subset_definition is not None and subset_definition not in self.subset_definitions:
+            self.subset_definitions = self.subset_definitions + [subset_definition]
+            self.subset_types = self.subset_types + [subset_type]
+
+    def _get_subset_definition(self, *args):
+        """
+        Retrieve the parameters defining the selected subset, for example the
+        upper and lower bounds for a simple spectral subset.
+        """
+        self.subset_definitions = []
+        self.subset_types = []
         subset_group = [s for s in self.app.data_collection.subset_groups if
                         s.label == self.subset_selected][0]
         subset_state = subset_group.subset_state
-        subset_class = subset_state.__class__
 
-        if subset_class in (OrState, AndState, XorState, InvertState):
-            self.subset_classname = "Compound Subset"
-            self.has_subset_details = False
-        else:
-            if isinstance(subset_state, RoiSubsetState):
-                self.subset_classname = subset_state.roi.__class__.__name__
-                self.has_subset_details = True
-                if self.subset_classname == "CircularROI":
-                    x, y = subset_state.roi.get_center()
-                    self.subset_definition = {"X Center": x,
-                                              "Y Center": y,
-                                              "Radius": subset_state.roi.radius}
-                elif self.subset_classname == "RectangularROI":
-                    temp_def = {}
-                    for att in ("Xmin", "Xmax", "Ymin", "Ymax"):
-                        temp_def[att] = getattr(subset_state.roi, att.lower())
-                    self.subset_definition = temp_def
-                elif self.subset_classname == "EllipticalROI":
-                    self.subset_definition = {"X Center": subset_state.roi.xc,
-                                              "Y Center": subset_state.roi.yc,
-                                              "X Radius": subset_state.roi.radius_x,
-                                              "Y Radius": subset_state.roi.radius_y}
-            elif isinstance(subset_state, RangeSubsetState):
-                self.subset_classname = "Range"
-                self.subset_definition = {"Upper bound": subset_state.hi,
-                                          "Lower bound": subset_state.lo}
-                self.has_subset_details = True
-            else:
-                self.subset_classname = subset_class.__name__
-                self.has_subset_details = False
+        self._unpack_nested_subset(subset_state)
diff --git a/jdaviz/configs/default/plugins/subset_plugin/subset_plugin.vue b/jdaviz/configs/default/plugins/subset_plugin/subset_plugin.vue
index 807b3f6e0f..93de7a32c4 100644
--- a/jdaviz/configs/default/plugins/subset_plugin/subset_plugin.vue
+++ b/jdaviz/configs/default/plugins/subset_plugin/subset_plugin.vue
@@ -27,24 +27,28 @@
 
     <div v-if="show_region_info">
       <j-plugin-section-header>Subset Region Definition</j-plugin-section-header>
-      <v-row>
-        <v-col>Subset Type: </v-col>
-        <v-col>{{ subset_classname }}</v-col>
       </v-row>
-      <div v-if="has_subset_details">
-        <v-row v-for="(val, key, index) in subset_definition">
-          <v-col>{{ key }}:</v-col> 
+      <div v-if="subset_definitions.length">
+        <v-row v-for="(subset_definition, index) in subset_definitions">
           <v-col>
-            <j-number-uncertainty
-              :value="val"
-              :defaultDigs="6"
-            ></j-number-uncertainty>
+            <v-row v-for="(val, key, index2) in subset_types[index]"
+             class="pt-0 pb-0 mt-0 mb-0">
+              <v-col>{{ key }}:</v-col>
+              <v-col>{{ val }}</v-col>
+            </v-row>
+            <v-row v-for="(val, key, index2) in subset_definition"
+             class="pt-0 pb-0 mt-0 mb-0">
+              <v-col>{{ key }}:</v-col>
+              <v-col>
+                <j-number-uncertainty
+                  :value="val"
+                  :defaultDigs="6"
+                ></j-number-uncertainty>
+              </v-col>
+            </v-row>
           </v-col>
         </v-row>
       </div>
-      <div v-else>
-        <v-row>Could not retrieve subset parameters for this subset type</v-row>
-      </div>
     </div>
   </j-tray-plugin>
 </template>
diff --git a/jdaviz/tests/test_subsets.py b/jdaviz/tests/test_subsets.py
index ca4241827d..6262aa3764 100644
--- a/jdaviz/tests/test_subsets.py
+++ b/jdaviz/tests/test_subsets.py
@@ -56,11 +56,11 @@ def test_region_from_subset_3d(cubeviz_helper):
     assert_allclose(reg.height, 3.5)
 
     assert subset_plugin.subset_selected == "Subset 1"
-    assert subset_plugin.subset_classname == "RectangularROI"
-    assert subset_plugin.subset_definition["Xmin"] == 1
-    assert subset_plugin.subset_definition["Xmax"] == 3.5
-    assert subset_plugin.subset_definition["Ymin"] == -0.2
-    assert subset_plugin.subset_definition["Ymax"] == 3.3
+    assert subset_plugin.subset_types == [{"Subset type": "RectangularROI"}]
+    assert subset_plugin.subset_definitions[0]["Xmin"] == 1
+    assert subset_plugin.subset_definitions[0]["Xmax"] == 3.5
+    assert subset_plugin.subset_definitions[0]["Ymin"] == -0.2
+    assert subset_plugin.subset_definitions[0]["Ymax"] == 3.3
 
     # Circular Subset
     flux_viewer = cubeviz_helper.app.get_viewer("flux-viewer")
@@ -68,10 +68,10 @@ def test_region_from_subset_3d(cubeviz_helper):
     flux_viewer.toolbar.active_tool = flux_viewer.toolbar.tools['bqplot:circle']
     cubeviz_helper.app.get_viewer('flux-viewer').apply_roi(CircularROI(xc=3, yc=4, radius=2.4))
     assert subset_plugin.subset_selected == "Subset 2"
-    assert subset_plugin.subset_classname == "CircularROI"
-    assert subset_plugin.subset_definition["X Center"] == 3
-    assert subset_plugin.subset_definition["Y Center"] == 4
-    assert subset_plugin.subset_definition["Radius"] == 2.4
+    assert subset_plugin.subset_types == [{"Subset type": "CircularROI"}]
+    assert subset_plugin.subset_definitions[0]["X Center"] == 3
+    assert subset_plugin.subset_definitions[0]["Y Center"] == 4
+    assert subset_plugin.subset_definitions[0]["Radius"] == 2.4
 
 
 def test_region_from_subset_profile(cubeviz_helper, spectral_cube_wcs):
@@ -93,9 +93,9 @@ def test_region_from_subset_profile(cubeviz_helper, spectral_cube_wcs):
     assert_quantity_allclose(reg.upper, 15.0 * u.Hz)
 
     assert subset_plugin.subset_selected == "Subset 1"
-    assert subset_plugin.subset_classname == "Range"
-    assert subset_plugin.subset_definition["Lower bound"] == 5
-    assert subset_plugin.subset_definition["Upper bound"] == 15.5
+    assert subset_plugin.subset_types == [{"Subset type": "Range"}]
+    assert subset_plugin.subset_definitions[0]["Lower bound"] == 5
+    assert subset_plugin.subset_definitions[0]["Upper bound"] == 15.5
 
 
 def test_region_spectral_spatial(cubeviz_helper, spectral_cube_wcs):
@@ -134,6 +134,7 @@ def test_region_spectral_spatial(cubeviz_helper, spectral_cube_wcs):
 
 
 def test_disjoint_spectral_subset(cubeviz_helper, spectral_cube_wcs):
+    subset_plugin = SubsetPlugin(app=cubeviz_helper.app)
     data = Data(flux=np.ones((128, 128, 256)), label='Test Flux', coords=spectral_cube_wcs)
     cubeviz_helper.app.data_collection.append(data)
 
@@ -156,3 +157,10 @@ def test_disjoint_spectral_subset(cubeviz_helper, spectral_cube_wcs):
     assert_quantity_allclose(reg[0].upper, 15.0*u.Hz)
     assert_quantity_allclose(reg[1].lower, 30.0*u.Hz)
     assert_quantity_allclose(reg[1].upper, 35.0*u.Hz)
+
+    assert subset_plugin.subset_selected == "Subset 1"
+    assert subset_plugin.subset_types == [{"Subset type": "Range"}, {"Subset type": "Range"}]
+    assert subset_plugin.subset_definitions[0]["Lower bound"] == 30
+    assert subset_plugin.subset_definitions[0]["Upper bound"] == 35
+    assert subset_plugin.subset_definitions[1]["Lower bound"] == 5
+    assert subset_plugin.subset_definitions[1]["Upper bound"] == 15.5