diff --git a/app/assets/javascripts/boards/components/board.js b/app/assets/javascripts/boards/components/board.js
index 45b9e57f9ab..c6122fbc686 100644
--- a/app/assets/javascripts/boards/components/board.js
+++ b/app/assets/javascripts/boards/components/board.js
@@ -1,6 +1,7 @@
+import $ from 'jquery';
 import Sortable from 'sortablejs';
 import Vue from 'vue';
-import { n__ } from '~/locale';
+import { n__, s__ } from '~/locale';
 import Icon from '~/vue_shared/components/icon.vue';
 import Tooltip from '~/vue_shared/directives/tooltip';
 import AccessorUtilities from '../../lib/utils/accessor';
@@ -53,12 +54,19 @@ export default Vue.extend({
       const { issuesSize } = this.list;
       return `${n__('%d issue', '%d issues', issuesSize)}`;
     },
+    caretTooltip() {
+      return this.list.isExpanded ? s__('Boards|Collapse') : s__('Boards|Expand');
+    },
     isNewIssueShown() {
       return (
         this.list.type === 'backlog' ||
         (!this.disabled && this.list.type !== 'closed' && this.list.type !== 'blank')
       );
     },
+    uniqueKey() {
+      // eslint-disable-next-line @gitlab/i18n/no-non-i18n-strings
+      return `boards.${this.boardId}.${this.list.type}.${this.list.id}`;
+    },
   },
   watch: {
     filter: {
@@ -72,31 +80,34 @@ export default Vue.extend({
     },
   },
   mounted() {
-    this.sortableOptions = getBoardSortableDefaultOptions({
+    const instance = this;
+
+    const sortableOptions = getBoardSortableDefaultOptions({
       disabled: this.disabled,
       group: 'boards',
       draggable: '.is-draggable',
       handle: '.js-board-handle',
-      onEnd: e => {
+      onEnd(e) {
         sortableEnd();
 
+        const sortable = this;
+
         if (e.newIndex !== undefined && e.oldIndex !== e.newIndex) {
-          const order = this.sortable.toArray();
+          const order = sortable.toArray();
           const list = boardsStore.findList('id', parseInt(e.item.dataset.id, 10));
 
-          this.$nextTick(() => {
+          instance.$nextTick(() => {
             boardsStore.moveList(list, order);
           });
         }
       },
     });
 
-    this.sortable = Sortable.create(this.$el.parentNode, this.sortableOptions);
+    Sortable.create(this.$el.parentNode, sortableOptions);
   },
   created() {
     if (this.list.isExpandable && AccessorUtilities.isLocalStorageAccessSafe()) {
-      const isCollapsed =
-        localStorage.getItem(`boards.${this.boardId}.${this.list.type}.expanded`) === 'false';
+      const isCollapsed = localStorage.getItem(`${this.uniqueKey}.expanded`) === 'false';
 
       this.list.isExpanded = !isCollapsed;
     }
@@ -105,16 +116,17 @@ export default Vue.extend({
     showNewIssueForm() {
       this.$refs['board-list'].showIssueForm = !this.$refs['board-list'].showIssueForm;
     },
-    toggleExpanded(e) {
-      if (this.list.isExpandable && !e.target.classList.contains('js-no-trigger-collapse')) {
+    toggleExpanded() {
+      if (this.list.isExpandable) {
         this.list.isExpanded = !this.list.isExpanded;
 
         if (AccessorUtilities.isLocalStorageAccessSafe()) {
-          localStorage.setItem(
-            `boards.${this.boardId}.${this.list.type}.expanded`,
-            this.list.isExpanded,
-          );
+          localStorage.setItem(`${this.uniqueKey}.expanded`, this.list.isExpanded);
         }
+
+        // When expanding/collapsing, the tooltip on the caret button sometimes stays open.
+        // Close all tooltips manually to prevent dangling tooltips.
+        $('.tooltip').tooltip('hide');
       }
     },
   },
diff --git a/app/assets/javascripts/boards/mixins/sortable_default_options.js b/app/assets/javascripts/boards/mixins/sortable_default_options.js
index 636ca99952c..68ea28e68d9 100644
--- a/app/assets/javascripts/boards/mixins/sortable_default_options.js
+++ b/app/assets/javascripts/boards/mixins/sortable_default_options.js
@@ -20,7 +20,7 @@ export function getBoardSortableDefaultOptions(obj) {
     'ontouchstart' in window || (window.DocumentTouch && document instanceof DocumentTouch);
 
   const defaultSortOptions = Object.assign({}, sortableConfig, {
-    filter: '.board-delete, .btn',
+    filter: '.no-drag',
     delay: touchEnabled ? 100 : 0,
     scrollSensitivity: touchEnabled ? 60 : 100,
     scrollSpeed: 20,
diff --git a/app/assets/javascripts/boards/models/list.js b/app/assets/javascripts/boards/models/list.js
index a9d88f19146..cd553d0c4af 100644
--- a/app/assets/javascripts/boards/models/list.js
+++ b/app/assets/javascripts/boards/models/list.js
@@ -26,6 +26,12 @@ const TYPES = {
     isExpandable: false,
     isBlank: true,
   },
+  default: {
+    // includes label, assignee, and milestone lists
+    isPreset: false,
+    isExpandable: true,
+    isBlank: false,
+  },
 };
 
 class List {
@@ -249,7 +255,7 @@ class List {
   }
 
   getTypeInfo(type) {
-    return TYPES[type] || {};
+    return TYPES[type] || TYPES.default;
   }
 
   onNewIssueResponse(issue, data) {
diff --git a/app/assets/stylesheets/pages/boards.scss b/app/assets/stylesheets/pages/boards.scss
index 5e3652db48f..343cca96851 100644
--- a/app/assets/stylesheets/pages/boards.scss
+++ b/app/assets/stylesheets/pages/boards.scss
@@ -92,9 +92,20 @@
     width: 400px;
   }
 
-  &.is-expandable {
-    .board-header {
-      cursor: pointer;
+  .board-title-caret {
+    cursor: pointer;
+    border-radius: $border-radius-default;
+    padding: 4px;
+
+    &:hover {
+      background-color: $gray-dark;
+      transition: background-color 0.1s linear;
+    }
+  }
+
+  &:not(.is-collapsed) {
+    .board-title-caret {
+      margin: 0 $gl-padding-4 0 -10px;
     }
   }
 
@@ -102,20 +113,51 @@
     width: 50px;
 
     .board-title {
-      > span {
-        width: 100%;
-        margin-top: -12px;
+      flex-direction: column;
+      height: 100%;
+      padding: $gl-padding-8 0;
+    }
+
+    .board-title-caret {
+      margin-top: 1px;
+    }
+
+    .user-avatar-link,
+    .milestone-icon {
+      margin-top: $gl-padding-8;
+      transform: rotate(90deg);
+    }
+
+    .board-title-text {
+      flex-grow: 0;
+      margin: $gl-padding-8 0;
+
+      .board-title-main-text {
         display: block;
-        transform: rotate(90deg) translate(35px, 0);
-        overflow: initial;
+      }
+
+      .board-title-sub-text {
+        display: none;
       }
     }
 
-    .board-title-expandable-toggle {
-      position: absolute;
-      top: 50%;
-      left: 50%;
-      margin-left: -10px;
+    .issue-count-badge {
+      border: 0;
+      white-space: nowrap;
+    }
+
+    .board-title-text > span,
+    .issue-count-badge > span {
+      height: 16px;
+
+      // Force the height to be equal to the parent's width while centering the contents.
+      // The contents *should* be about 16 px.
+      // We do this because the flow of elements isn't affected by the rotate transform, so we must ensure that a
+      // rotated element has square dimensions so it won't overlap with its siblings.
+      margin: calc(50% - 8px) 0;
+
+      transform: rotate(90deg);
+      transform-origin: center;
     }
   }
 }
@@ -152,12 +194,14 @@
 }
 
 .board-title {
+  align-items: center;
   font-size: 1em;
   border-bottom: 1px solid $border-color;
+  padding: $gl-padding-8 $gl-padding;
 }
 
 .board-title-text {
-  margin: $gl-vert-padding auto $gl-vert-padding 0;
+  flex-grow: 1;
 }
 
 .board-delete {
diff --git a/app/views/shared/boards/components/_board.html.haml b/app/views/shared/boards/components/_board.html.haml
index f9cfcabc015..fdb2a0a1843 100644
--- a/app/views/shared/boards/components/_board.html.haml
+++ b/app/views/shared/boards/components/_board.html.haml
@@ -1,52 +1,60 @@
 .board.d-inline-block.h-100.px-2.align-top.ws-normal{ ":class" => '{ "is-draggable": !list.preset, "is-expandable": list.isExpandable, "is-collapsed": !list.isExpanded, "board-type-assignee": list.type === "assignee" }',
   ":data-id" => "list.id" }
   .board-inner.d-flex.flex-column.position-relative.h-100.rounded
-    %header.board-header{ ":class" => '{ "has-border": list.label && list.label.color, "position-relative": list.isExpanded, "position-absolute position-top-0 position-left-0 w-100 h-100": !list.isExpanded }', ":style" => "{ borderTopColor: (list.label && list.label.color ? list.label.color : null) }", "@click" => "toggleExpanded($event)" }
-      %h3.board-title.m-0.d-flex.align-items-center.py-2.px-3.js-board-handle{ ":class" => '{ "user-can-drag": (!disabled && !list.preset), "p-0 border-bottom-0 justify-content-center": !list.isExpanded }' }
-        %i.fa.fa-fw.board-title-expandable-toggle{ "v-if": "list.isExpandable",
-          ":class": "{ \"fa-caret-down\": list.isExpanded, \"fa-caret-right\": !list.isExpanded }",
-          "aria-hidden": "true" }
+    %header.board-header{ ":class" => '{ "has-border": list.label && list.label.color, "position-relative": list.isExpanded, "position-absolute position-top-0 position-left-0 w-100 h-100": !list.isExpanded }', ":style" => "{ borderTopColor: (list.label && list.label.color ? list.label.color : null) }" }
+      %h3.board-title.m-0.d-flex.js-board-handle{ ":class" => '{ "user-can-drag": (!disabled && !list.preset), "border-bottom-0": !list.isExpanded }' }
+
+        .board-title-caret.no-drag{ "v-if": "list.isExpandable",
+          "aria-hidden": "true",
+          ":aria-label": "caretTooltip",
+          ":title": "caretTooltip",
+          "v-tooltip": "",
+          data: { placement: "bottom" },
+          "@click": "toggleExpanded" }
+          %i.fa.fa-fw{ ":class": '{ "fa-caret-right": list.isExpanded, "fa-caret-down": !list.isExpanded }' }
         = render_if_exists "shared/boards/components/list_milestone"
 
         %a.user-avatar-link.js-no-trigger{ "v-if": "list.type === \"assignee\"", ":href": "list.assignee.path" }
           -# haml-lint:disable AltText
           %img.avatar.s20.has-tooltip{ height: "20", width: "20", ":src": "list.assignee.avatar", ":alt": "list.assignee.name" }
 
-        %span.board-title-text.has-tooltip.block-truncated{ "v-if": "list.type !== \"label\"",
-          ":title" => '((list.label && list.label.description) || list.title || "")', data: { container: "body" } }
-          {{ list.title }}
+        .board-title-text
+          %span.board-title-main-text.has-tooltip.block-truncated{ "v-if": "list.type !== \"label\"",
+            ":title" => '((list.label && list.label.description) || list.title || "")', data: { container: "body" } }
+            {{ list.title }}
 
-        %span.board-title-sub-text.prepend-left-5.has-tooltip{ "v-if": "list.type === \"assignee\"",
-          ":title" => '(list.assignee && list.assignee.username || "")' }
-          @{{ list.assignee.username }}
+          %span.board-title-sub-text.prepend-left-5.has-tooltip{ "v-if": "list.type === \"assignee\"",
+            ":title" => '(list.assignee && list.assignee.username || "")' }
+            @{{ list.assignee.username }}
 
-        %span.has-tooltip{ "v-if": "list.type === \"label\"",
-          ":title" => '(list.label ? list.label.description : "")',
-          data: { container: "body", placement: "bottom" },
-          class: "badge color-label title board-title-text",
-          ":style" => "{ backgroundColor: (list.label && list.label.color ? list.label.color : null), color: (list.label && list.label.textColor ? list.label.textColor : \"#2e2e2e\") }" }
-          {{ list.title }}
+          %span.has-tooltip.badge.color-label.title{ "v-if": "list.type === \"label\"",
+            ":title" => '(list.label ? list.label.description : "")',
+            data: { container: "body", placement: "bottom" },
+            ":style" => "{ backgroundColor: (list.label && list.label.color ? list.label.color : null), color: (list.label && list.label.textColor ? list.label.textColor : \"#2e2e2e\") }" }
+            {{ list.title }}
 
         - if can?(current_user, :admin_list, current_board_parent)
           %board-delete{ "inline-template" => true,
             ":list" => "list",
             "v-if" => "!list.preset && list.id" }
-            %button.board-delete.p-0.border-0.has-tooltip.float-right{ type: "button", title: _("Delete list"), ":class": "{ 'd-none': !list.isExpanded }", "aria-label" => _("Delete list"), data: { placement: "bottom" }, "@click.stop" => "deleteBoard" }
+            %button.board-delete.no-drag.p-0.border-0.has-tooltip.float-right{ type: "button", title: _("Delete list"), ":class": "{ 'd-none': !list.isExpanded }", "aria-label" => _("Delete list"), data: { placement: "bottom" }, "@click.stop" => "deleteBoard" }
               = icon("trash")
-        .issue-count-badge.text-secondary{ "v-if" => 'list.type !== "blank" && list.type !== "promotion"', ":title": "counterTooltip", ":class": "{ 'd-none': !list.isExpanded }", "v-tooltip": true, data: { placement: "top" } }
-          %span.issue-count-badge-count
-            %icon.mr-1{ name: "issues" }
-            {{ list.issuesSize }}
-          = render_if_exists "shared/boards/components/list_weight"
 
-        %button.issue-count-badge-add-button.btn.btn-sm.btn-default.ml-1.has-tooltip.js-no-trigger-collapse{ type: "button",
+        .issue-count-badge.no-drag.text-secondary{ "v-if" => 'list.type !== "blank" && list.type !== "promotion"', ":title": "counterTooltip", "v-tooltip": true, data: { placement: "top" } }
+          %span.d-inline-flex
+            %span.issue-count-badge-count
+              %icon.mr-1{ name: "issues" }
+              {{ list.issuesSize }}
+            = render_if_exists "shared/boards/components/list_weight"
+
+        %button.issue-count-badge-add-button.no-drag.btn.btn-sm.btn-default.ml-1.has-tooltip{ type: "button",
           "@click" => "showNewIssueForm",
           "v-if" => "isNewIssueShown",
           ":class": "{ 'd-none': !list.isExpanded }",
           "aria-label" => _("New issue"),
           "title" => _("New issue"),
           data: { placement: "top", container: "body" } }
-          = icon("plus", class: "js-no-trigger-collapse")
+          = icon("plus")
 
     %board-list{ "v-if" => 'list.type !== "blank" && list.type !== "promotion"',
       ":list" => "list",
diff --git a/changelogs/unreleased/mh-collapsible-boards.yml b/changelogs/unreleased/mh-collapsible-boards.yml
new file mode 100644
index 00000000000..b69d6e81cc4
--- /dev/null
+++ b/changelogs/unreleased/mh-collapsible-boards.yml
@@ -0,0 +1,5 @@
+---
+title: Labeled issue boards can now collapse
+merge_request: 29955
+author:
+type: added
diff --git a/locale/gitlab.pot b/locale/gitlab.pot
index 840664298d3..a04a0acd98e 100644
--- a/locale/gitlab.pot
+++ b/locale/gitlab.pot
@@ -1606,6 +1606,12 @@ msgstr ""
 msgid "Boards"
 msgstr ""
 
+msgid "Boards|Collapse"
+msgstr ""
+
+msgid "Boards|Expand"
+msgstr ""
+
 msgid "Branch %{branchName} was not found in this project's repository."
 msgstr ""
 
diff --git a/spec/javascripts/boards/components/board_spec.js b/spec/javascripts/boards/components/board_spec.js
index d08ee41802b..683783334c6 100644
--- a/spec/javascripts/boards/components/board_spec.js
+++ b/spec/javascripts/boards/components/board_spec.js
@@ -1,7 +1,6 @@
 import Vue from 'vue';
-import '~/boards/services/board_service';
 import Board from '~/boards/components/board';
-import '~/boards/models/list';
+import List from '~/boards/models/list';
 import { mockBoardService } from '../mock_data';
 
 describe('Board component', () => {
@@ -27,7 +26,6 @@ describe('Board component', () => {
         disabled: false,
         issueLinkBase: '/',
         rootPath: '/',
-        // eslint-disable-next-line no-undef
         list: new List({
           id: 1,
           position: 0,
@@ -53,57 +51,62 @@ describe('Board component', () => {
     expect(vm.$el.classList.contains('is-expandable')).toBe(true);
   });
 
-  it('board is expandable when list type is closed', done => {
-    vm.list.type = 'closed';
-
-    Vue.nextTick(() => {
-      expect(vm.$el.classList.contains('is-expandable')).toBe(true);
-
-      done();
-    });
+  it('board is expandable when list type is closed', () => {
+    expect(new List({ id: 1, list_type: 'closed' }).isExpandable).toBe(true);
   });
 
-  it('board is not expandable when list type is label', done => {
-    vm.list.type = 'label';
-    vm.list.isExpandable = false;
-
-    Vue.nextTick(() => {
-      expect(vm.$el.classList.contains('is-expandable')).toBe(false);
-
-      done();
-    });
+  it('board is expandable when list type is label', () => {
+    expect(new List({ id: 1, list_type: 'closed' }).isExpandable).toBe(true);
   });
 
-  it('collapses when clicking header', done => {
+  it('board is not expandable when list type is blank', () => {
+    expect(new List({ id: 1, list_type: 'blank' }).isExpandable).toBe(false);
+  });
+
+  it('does not collapse when clicking header', done => {
+    vm.list.isExpanded = true;
     vm.$el.querySelector('.board-header').click();
 
     Vue.nextTick(() => {
-      expect(vm.$el.classList.contains('is-collapsed')).toBe(true);
+      expect(vm.$el.classList.contains('is-collapsed')).toBe(false);
 
       done();
     });
   });
 
-  it('created sets isExpanded to true from localStorage', done => {
-    vm.$el.querySelector('.board-header').click();
+  it('collapses when clicking the collapse icon', done => {
+    vm.list.isExpanded = true;
 
-    return Vue.nextTick()
+    Vue.nextTick()
       .then(() => {
-        expect(vm.$el.classList.contains('is-collapsed')).toBe(true);
-
-        // call created manually
-        vm.$options.created[0].call(vm);
-
-        return Vue.nextTick();
+        vm.$el.querySelector('.board-title-caret').click();
       })
       .then(() => {
         expect(vm.$el.classList.contains('is-collapsed')).toBe(true);
-
         done();
       })
       .catch(done.fail);
   });
 
+  it('expands when clicking the expand icon', done => {
+    vm.list.isExpanded = false;
+
+    Vue.nextTick()
+      .then(() => {
+        vm.$el.querySelector('.board-title-caret').click();
+      })
+      .then(() => {
+        expect(vm.$el.classList.contains('is-collapsed')).toBe(false);
+        done();
+      })
+      .catch(done.fail);
+  });
+
+  it('is expanded when created', () => {
+    expect(vm.list.isExpanded).toBe(true);
+    expect(vm.$el.classList.contains('is-collapsed')).toBe(false);
+  });
+
   it('does render add issue button', () => {
     expect(vm.$el.querySelector('.issue-count-badge-add-button')).not.toBeNull();
   });