diff --git a/app/assets/javascripts/vue_shared/components/issue/issue_milestone.vue b/app/assets/javascripts/vue_shared/components/issue/issue_milestone.vue
index 1f9670cf2fc..53e6efa6ea3 100644
--- a/app/assets/javascripts/vue_shared/components/issue/issue_milestone.vue
+++ b/app/assets/javascripts/vue_shared/components/issue/issue_milestone.vue
@@ -17,15 +17,13 @@ export default {
       required: true,
     },
   },
-  data() {
-    return {
-      milestoneDue: this.milestone.due_date ? parsePikadayDate(this.milestone.due_date) : null,
-      milestoneStart: this.milestone.start_date
-        ? parsePikadayDate(this.milestone.start_date)
-        : null,
-    };
-  },
   computed: {
+    milestoneDue() {
+      return this.milestone.due_date ? parsePikadayDate(this.milestone.due_date) : null;
+    },
+    milestoneStart() {
+      return this.milestone.start_date ? parsePikadayDate(this.milestone.start_date) : null;
+    },
     isMilestoneStarted() {
       if (!this.milestoneStart) {
         return false;
diff --git a/app/assets/javascripts/vue_shared/components/issue/related_issuable_item.vue b/app/assets/javascripts/vue_shared/components/issue/related_issuable_item.vue
index ffde55bf083..b807a35b421 100644
--- a/app/assets/javascripts/vue_shared/components/issue/related_issuable_item.vue
+++ b/app/assets/javascripts/vue_shared/components/issue/related_issuable_item.vue
@@ -1,4 +1,5 @@
 <script>
+import '~/commons/bootstrap';
 import { GlTooltipDirective } from '@gitlab/ui';
 import { sprintf } from '~/locale';
 import IssueMilestone from '../../components/issue/issue_milestone.vue';
diff --git a/changelogs/unreleased/refactor-58827-migrate-issue-spec-to-jest.yml b/changelogs/unreleased/refactor-58827-migrate-issue-spec-to-jest.yml
new file mode 100644
index 00000000000..03d94c39c10
--- /dev/null
+++ b/changelogs/unreleased/refactor-58827-migrate-issue-spec-to-jest.yml
@@ -0,0 +1,5 @@
+---
+title: 'refactor(issue): Refactored issue tests from Karma to Jest'
+merge_request: 27673
+author: Martin Hobert
+type: other
diff --git a/spec/javascripts/vue_shared/components/issue/issue_assignees_spec.js b/spec/frontend/vue_shared/components/issue/issue_assignees_spec.js
similarity index 96%
rename from spec/javascripts/vue_shared/components/issue/issue_assignees_spec.js
rename to spec/frontend/vue_shared/components/issue/issue_assignees_spec.js
index 9eac75fac96..d1de98f4a15 100644
--- a/spec/javascripts/vue_shared/components/issue/issue_assignees_spec.js
+++ b/spec/frontend/vue_shared/components/issue/issue_assignees_spec.js
@@ -2,8 +2,8 @@ import Vue from 'vue';
 
 import IssueAssignees from '~/vue_shared/components/issue/issue_assignees.vue';
 
-import mountComponent from 'spec/helpers/vue_mount_component_helper';
-import { mockAssigneesList } from 'spec/boards/mock_data';
+import mountComponent from 'helpers/vue_mount_component_helper';
+import { mockAssigneesList } from '../../../../javascripts/boards/mock_data';
 
 const createComponent = (assignees = mockAssigneesList, cssClass = '') => {
   const Component = Vue.extend(IssueAssignees);
diff --git a/spec/frontend/vue_shared/components/issue/issue_milestone_spec.js b/spec/frontend/vue_shared/components/issue/issue_milestone_spec.js
new file mode 100644
index 00000000000..2e93ec412b9
--- /dev/null
+++ b/spec/frontend/vue_shared/components/issue/issue_milestone_spec.js
@@ -0,0 +1,172 @@
+import Vue from 'vue';
+import { mount } from '@vue/test-utils';
+
+import IssueMilestone from '~/vue_shared/components/issue/issue_milestone.vue';
+
+import { mockMilestone } from '../../../../javascripts/boards/mock_data';
+
+const createComponent = (milestone = mockMilestone) => {
+  const Component = Vue.extend(IssueMilestone);
+
+  return mount(Component, {
+    propsData: {
+      milestone,
+    },
+    sync: false,
+  });
+};
+
+describe('IssueMilestoneComponent', () => {
+  let wrapper;
+  let vm;
+
+  beforeEach(done => {
+    wrapper = createComponent();
+
+    ({ vm } = wrapper);
+
+    Vue.nextTick(done);
+  });
+
+  afterEach(() => {
+    wrapper.destroy();
+  });
+
+  describe('computed', () => {
+    describe('isMilestoneStarted', () => {
+      it('should return `false` when milestoneStart prop is not defined', () => {
+        wrapper.setProps({
+          milestone: Object.assign({}, mockMilestone, {
+            start_date: '',
+          }),
+        });
+
+        expect(wrapper.vm.isMilestoneStarted).toBe(false);
+      });
+
+      it('should return `true` when milestone start date is past current date', () => {
+        wrapper.setProps({
+          milestone: Object.assign({}, mockMilestone, {
+            start_date: '1990-07-22',
+          }),
+        });
+
+        expect(wrapper.vm.isMilestoneStarted).toBe(true);
+      });
+    });
+
+    describe('isMilestonePastDue', () => {
+      it('should return `false` when milestoneDue prop is not defined', () => {
+        wrapper.setProps({
+          milestone: Object.assign({}, mockMilestone, {
+            due_date: '',
+          }),
+        });
+
+        expect(wrapper.vm.isMilestonePastDue).toBe(false);
+      });
+
+      it('should return `true` when milestone due is past current date', () => {
+        wrapper.setProps({
+          milestone: Object.assign({}, mockMilestone, {
+            due_date: '1990-07-22',
+          }),
+        });
+
+        expect(wrapper.vm.isMilestonePastDue).toBe(true);
+      });
+    });
+
+    describe('milestoneDatesAbsolute', () => {
+      it('returns string containing absolute milestone due date', () => {
+        expect(vm.milestoneDatesAbsolute).toBe('(December 31, 2019)');
+      });
+
+      it('returns string containing absolute milestone start date when due date is not present', () => {
+        wrapper.setProps({
+          milestone: Object.assign({}, mockMilestone, {
+            due_date: '',
+          }),
+        });
+
+        expect(wrapper.vm.milestoneDatesAbsolute).toBe('(January 1, 2018)');
+      });
+
+      it('returns empty string when both milestone start and due dates are not present', () => {
+        wrapper.setProps({
+          milestone: Object.assign({}, mockMilestone, {
+            start_date: '',
+            due_date: '',
+          }),
+        });
+
+        expect(wrapper.vm.milestoneDatesAbsolute).toBe('');
+      });
+    });
+
+    describe('milestoneDatesHuman', () => {
+      it('returns string containing milestone due date when date is yet to be due', () => {
+        wrapper.setProps({
+          milestone: Object.assign({}, mockMilestone, {
+            due_date: `${new Date().getFullYear() + 10}-01-01`,
+          }),
+        });
+
+        expect(wrapper.vm.milestoneDatesHuman).toContain('years remaining');
+      });
+
+      it('returns string containing milestone start date when date has already started and due date is not present', () => {
+        wrapper.setProps({
+          milestone: Object.assign({}, mockMilestone, {
+            start_date: '1990-07-22',
+            due_date: '',
+          }),
+        });
+
+        expect(wrapper.vm.milestoneDatesHuman).toContain('Started');
+      });
+
+      it('returns string containing milestone start date when date is yet to start and due date is not present', () => {
+        wrapper.setProps({
+          milestone: Object.assign({}, mockMilestone, {
+            start_date: `${new Date().getFullYear() + 10}-01-01`,
+            due_date: '',
+          }),
+        });
+
+        expect(wrapper.vm.milestoneDatesHuman).toContain('Starts');
+      });
+
+      it('returns empty string when milestone start and due dates are not present', () => {
+        wrapper.setProps({
+          milestone: Object.assign({}, mockMilestone, {
+            start_date: '',
+            due_date: '',
+          }),
+        });
+
+        expect(wrapper.vm.milestoneDatesHuman).toBe('');
+      });
+    });
+  });
+
+  describe('template', () => {
+    it('renders component root element with class `issue-milestone-details`', () => {
+      expect(vm.$el.classList.contains('issue-milestone-details')).toBe(true);
+    });
+
+    it('renders milestone icon', () => {
+      expect(vm.$el.querySelector('svg use').getAttribute('xlink:href')).toContain('clock');
+    });
+
+    it('renders milestone title', () => {
+      expect(vm.$el.querySelector('.milestone-title').innerText.trim()).toBe(mockMilestone.title);
+    });
+
+    it('renders milestone tooltip', () => {
+      expect(vm.$el.querySelector('.js-item-milestone').innerText.trim()).toContain(
+        mockMilestone.title,
+      );
+    });
+  });
+});
diff --git a/spec/javascripts/vue_shared/components/issue/issue_warning_spec.js b/spec/frontend/vue_shared/components/issue/issue_warning_spec.js
similarity index 82%
rename from spec/javascripts/vue_shared/components/issue/issue_warning_spec.js
rename to spec/frontend/vue_shared/components/issue/issue_warning_spec.js
index aa7d6ea2e34..4a8de5fc4f1 100644
--- a/spec/javascripts/vue_shared/components/issue/issue_warning_spec.js
+++ b/spec/frontend/vue_shared/components/issue/issue_warning_spec.js
@@ -1,6 +1,6 @@
 import Vue from 'vue';
 import issueWarning from '~/vue_shared/components/issue/issue_warning.vue';
-import mountComponent from 'spec/helpers/vue_mount_component_helper';
+import mountComponent from 'helpers/vue_mount_component_helper';
 
 const IssueWarning = Vue.extend(issueWarning);
 
@@ -19,7 +19,9 @@ describe('Issue Warning Component', () => {
         isLocked: true,
       });
 
-      expect(vm.$el.querySelector('.icon use').href.baseVal).toMatch(/lock$/);
+      expect(
+        vm.$el.querySelector('.icon use').getAttributeNS('http://www.w3.org/1999/xlink', 'href'),
+      ).toMatch(/lock$/);
       expect(formatWarning(vm.$el.querySelector('span').textContent)).toEqual(
         'This issue is locked. Only project members can comment.',
       );
@@ -32,7 +34,9 @@ describe('Issue Warning Component', () => {
         isConfidential: true,
       });
 
-      expect(vm.$el.querySelector('.icon use').href.baseVal).toMatch(/eye-slash$/);
+      expect(
+        vm.$el.querySelector('.icon use').getAttributeNS('http://www.w3.org/1999/xlink', 'href'),
+      ).toMatch(/eye-slash$/);
       expect(formatWarning(vm.$el.querySelector('span').textContent)).toEqual(
         'This is a confidential issue. Your comment will not be visible to the public.',
       );
diff --git a/spec/javascripts/vue_shared/components/issue/related_issuable_item_spec.js b/spec/frontend/vue_shared/components/issue/related_issuable_item_spec.js
similarity index 93%
rename from spec/javascripts/vue_shared/components/issue/related_issuable_item_spec.js
rename to spec/frontend/vue_shared/components/issue/related_issuable_item_spec.js
index 42198e92eea..e43d5301a50 100644
--- a/spec/javascripts/vue_shared/components/issue/related_issuable_item_spec.js
+++ b/spec/frontend/vue_shared/components/issue/related_issuable_item_spec.js
@@ -1,7 +1,11 @@
 import Vue from 'vue';
+import { formatDate } from '~/lib/utils/datetime_utility';
 import { mount, createLocalVue } from '@vue/test-utils';
 import RelatedIssuableItem from '~/vue_shared/components/issue/related_issuable_item.vue';
-import { defaultMilestone, defaultAssignees } from './related_issuable_mock_data';
+import {
+  defaultAssignees,
+  defaultMilestone,
+} from '../../../../javascripts/vue_shared/components/issue/related_issuable_mock_data';
 
 describe('RelatedIssuableItem', () => {
   let wrapper;
@@ -85,11 +89,11 @@ describe('RelatedIssuableItem', () => {
 
     it('renders state title', () => {
       const stateTitle = tokenState.attributes('data-original-title');
+      const formatedCreateDate = formatDate(props.createdAt);
 
       expect(stateTitle).toContain('<span class="bold">Opened</span>');
-      expect(stateTitle).toContain(
-        '<span class="text-tertiary">Dec 1, 2018 12:00am GMT+0000</span>',
-      );
+
+      expect(stateTitle).toContain(`<span class="text-tertiary">${formatedCreateDate}</span>`);
     });
 
     it('renders aria label', () => {
diff --git a/spec/javascripts/vue_shared/components/issue/issue_milestone_spec.js b/spec/javascripts/vue_shared/components/issue/issue_milestone_spec.js
deleted file mode 100644
index 8fca2637326..00000000000
--- a/spec/javascripts/vue_shared/components/issue/issue_milestone_spec.js
+++ /dev/null
@@ -1,234 +0,0 @@
-import Vue from 'vue';
-
-import IssueMilestone from '~/vue_shared/components/issue/issue_milestone.vue';
-
-import mountComponent from 'spec/helpers/vue_mount_component_helper';
-import { mockMilestone } from 'spec/boards/mock_data';
-
-const createComponent = (milestone = mockMilestone) => {
-  const Component = Vue.extend(IssueMilestone);
-
-  return mountComponent(Component, {
-    milestone,
-  });
-};
-
-describe('IssueMilestoneComponent', () => {
-  let vm;
-
-  beforeEach(() => {
-    vm = createComponent();
-  });
-
-  afterEach(() => {
-    vm.$destroy();
-  });
-
-  describe('computed', () => {
-    describe('isMilestoneStarted', () => {
-      it('should return `false` when milestoneStart prop is not defined', done => {
-        const vmStartUndefined = createComponent(
-          Object.assign({}, mockMilestone, {
-            start_date: '',
-          }),
-        );
-
-        Vue.nextTick()
-          .then(() => {
-            expect(vmStartUndefined.isMilestoneStarted).toBe(false);
-          })
-          .then(done)
-          .catch(done.fail);
-
-        vmStartUndefined.$destroy();
-      });
-
-      it('should return `true` when milestone start date is past current date', done => {
-        const vmStarted = createComponent(
-          Object.assign({}, mockMilestone, {
-            start_date: '1990-07-22',
-          }),
-        );
-
-        Vue.nextTick()
-          .then(() => {
-            expect(vmStarted.isMilestoneStarted).toBe(true);
-          })
-          .then(done)
-          .catch(done.fail);
-
-        vmStarted.$destroy();
-      });
-    });
-
-    describe('isMilestonePastDue', () => {
-      it('should return `false` when milestoneDue prop is not defined', done => {
-        const vmDueUndefined = createComponent(
-          Object.assign({}, mockMilestone, {
-            due_date: '',
-          }),
-        );
-
-        Vue.nextTick()
-          .then(() => {
-            expect(vmDueUndefined.isMilestonePastDue).toBe(false);
-          })
-          .then(done)
-          .catch(done.fail);
-
-        vmDueUndefined.$destroy();
-      });
-
-      it('should return `true` when milestone due is past current date', done => {
-        const vmPastDue = createComponent(
-          Object.assign({}, mockMilestone, {
-            due_date: '1990-07-22',
-          }),
-        );
-
-        Vue.nextTick()
-          .then(() => {
-            expect(vmPastDue.isMilestonePastDue).toBe(true);
-          })
-          .then(done)
-          .catch(done.fail);
-
-        vmPastDue.$destroy();
-      });
-    });
-
-    describe('milestoneDatesAbsolute', () => {
-      it('returns string containing absolute milestone due date', () => {
-        expect(vm.milestoneDatesAbsolute).toBe('(December 31, 2019)');
-      });
-
-      it('returns string containing absolute milestone start date when due date is not present', done => {
-        const vmDueUndefined = createComponent(
-          Object.assign({}, mockMilestone, {
-            due_date: '',
-          }),
-        );
-
-        Vue.nextTick()
-          .then(() => {
-            expect(vmDueUndefined.milestoneDatesAbsolute).toBe('(January 1, 2018)');
-          })
-          .then(done)
-          .catch(done.fail);
-
-        vmDueUndefined.$destroy();
-      });
-
-      it('returns empty string when both milestone start and due dates are not present', done => {
-        const vmDatesUndefined = createComponent(
-          Object.assign({}, mockMilestone, {
-            start_date: '',
-            due_date: '',
-          }),
-        );
-
-        Vue.nextTick()
-          .then(() => {
-            expect(vmDatesUndefined.milestoneDatesAbsolute).toBe('');
-          })
-          .then(done)
-          .catch(done.fail);
-
-        vmDatesUndefined.$destroy();
-      });
-    });
-
-    describe('milestoneDatesHuman', () => {
-      it('returns string containing milestone due date when date is yet to be due', done => {
-        const vmFuture = createComponent(
-          Object.assign({}, mockMilestone, {
-            due_date: `${new Date().getFullYear() + 10}-01-01`,
-          }),
-        );
-
-        Vue.nextTick()
-          .then(() => {
-            expect(vmFuture.milestoneDatesHuman).toContain('years remaining');
-          })
-          .then(done)
-          .catch(done.fail);
-
-        vmFuture.$destroy();
-      });
-
-      it('returns string containing milestone start date when date has already started and due date is not present', done => {
-        const vmStarted = createComponent(
-          Object.assign({}, mockMilestone, {
-            start_date: '1990-07-22',
-            due_date: '',
-          }),
-        );
-
-        Vue.nextTick()
-          .then(() => {
-            expect(vmStarted.milestoneDatesHuman).toContain('Started');
-          })
-          .then(done)
-          .catch(done.fail);
-
-        vmStarted.$destroy();
-      });
-
-      it('returns string containing milestone start date when date is yet to start and due date is not present', done => {
-        const vmStarts = createComponent(
-          Object.assign({}, mockMilestone, {
-            start_date: `${new Date().getFullYear() + 10}-01-01`,
-            due_date: '',
-          }),
-        );
-
-        Vue.nextTick()
-          .then(() => {
-            expect(vmStarts.milestoneDatesHuman).toContain('Starts');
-          })
-          .then(done)
-          .catch(done.fail);
-
-        vmStarts.$destroy();
-      });
-
-      it('returns empty string when milestone start and due dates are not present', done => {
-        const vmDatesUndefined = createComponent(
-          Object.assign({}, mockMilestone, {
-            start_date: '',
-            due_date: '',
-          }),
-        );
-
-        Vue.nextTick()
-          .then(() => {
-            expect(vmDatesUndefined.milestoneDatesHuman).toBe('');
-          })
-          .then(done)
-          .catch(done.fail);
-
-        vmDatesUndefined.$destroy();
-      });
-    });
-  });
-
-  describe('template', () => {
-    it('renders component root element with class `issue-milestone-details`', () => {
-      expect(vm.$el.classList.contains('issue-milestone-details')).toBe(true);
-    });
-
-    it('renders milestone icon', () => {
-      expect(vm.$el.querySelector('svg use').getAttribute('xlink:href')).toContain('clock');
-    });
-
-    it('renders milestone title', () => {
-      expect(vm.$el.querySelector('.milestone-title').innerText.trim()).toBe(mockMilestone.title);
-    });
-
-    it('renders milestone tooltip', () => {
-      expect(vm.$el.querySelector('.js-item-milestone').innerText.trim()).toContain(
-        mockMilestone.title,
-      );
-    });
-  });
-});