diff --git a/packages/@headlessui-react/src/components/combobox/combobox.test.tsx b/packages/@headlessui-react/src/components/combobox/combobox.test.tsx
index 0692d1e..8284245 100644
--- a/packages/@headlessui-react/src/components/combobox/combobox.test.tsx
+++ b/packages/@headlessui-react/src/components/combobox/combobox.test.tsx
@@ -171,7 +171,7 @@ describe('Rendering', () => {
       })
     )
 
-    describe.skip('Equality', () => {
+    describe('Equality', () => {
       let options = [
         { id: 1, name: 'Alice' },
         { id: 2, name: 'Bob' },
diff --git a/packages/@headlessui-react/src/components/combobox/combobox.tsx b/packages/@headlessui-react/src/components/combobox/combobox.tsx
index 1e86ad0..df98d32 100644
--- a/packages/@headlessui-react/src/components/combobox/combobox.tsx
+++ b/packages/@headlessui-react/src/components/combobox/combobox.tsx
@@ -311,10 +311,11 @@ let ComboboxRoot = forwardRefWithAs(function Combobox<
   props: Props<
     TTag,
     ComboboxRenderPropArg<TType>,
-    'value' | 'onChange' | 'disabled' | 'name' | 'nullable' | 'multiple'
+    'value' | 'onChange' | 'disabled' | 'name' | 'nullable' | 'multiple' | 'by'
   > & {
     value: TType
     onChange(value: TType): void
+    by?: (keyof TType & string) | ((a: TType, z: TType) => boolean)
     disabled?: boolean
     __demoMode?: boolean
     name?: string
@@ -327,6 +328,7 @@ let ComboboxRoot = forwardRefWithAs(function Combobox<
     name,
     value,
     onChange: theirOnChange,
+    by = (a, z) => a === z,
     disabled = false,
     __demoMode = false,
     nullable = false,
@@ -352,7 +354,14 @@ let ComboboxRoot = forwardRefWithAs(function Combobox<
   let buttonRef = useRef<_Data['buttonRef']['current']>(null)
   let optionsRef = useRef<_Data['optionsRef']['current']>(null)
 
-  let compare = useEvent((a, z) => a === z)
+  let compare = useEvent(
+    typeof by === 'string'
+      ? (a: TType, z: TType) => {
+          let property = by as unknown as keyof TType
+          return a[property] === z[property]
+        }
+      : by
+  )
 
   let isSelected: (value: TType) => boolean = useCallback(
     (compareValue) =>
diff --git a/packages/@headlessui-react/src/components/listbox/listbox.test.tsx b/packages/@headlessui-react/src/components/listbox/listbox.test.tsx
index 0c9c487..8fe7eb1 100644
--- a/packages/@headlessui-react/src/components/listbox/listbox.test.tsx
+++ b/packages/@headlessui-react/src/components/listbox/listbox.test.tsx
@@ -163,7 +163,7 @@ describe('Rendering', () => {
       })
     )
 
-    describe.skip('Equality', () => {
+    describe('Equality', () => {
       let options = [
         { id: 1, name: 'Alice' },
         { id: 2, name: 'Bob' },
diff --git a/packages/@headlessui-react/src/components/listbox/listbox.tsx b/packages/@headlessui-react/src/components/listbox/listbox.tsx
index a4803b9..b664331 100644
--- a/packages/@headlessui-react/src/components/listbox/listbox.tsx
+++ b/packages/@headlessui-react/src/components/listbox/listbox.tsx
@@ -311,10 +311,11 @@ let ListboxRoot = forwardRefWithAs(function Listbox<
   props: Props<
     TTag,
     ListboxRenderPropArg,
-    'value' | 'onChange' | 'disabled' | 'horizontal' | 'name' | 'multiple'
+    'value' | 'onChange' | 'disabled' | 'horizontal' | 'name' | 'multiple' | 'by'
   > & {
     value: TType
     onChange(value: TType): void
+    by?: (keyof TType & string) | ((a: TType, z: TType) => boolean)
     disabled?: boolean
     horizontal?: boolean
     name?: string
@@ -326,6 +327,7 @@ let ListboxRoot = forwardRefWithAs(function Listbox<
     value,
     name,
     onChange,
+    by = (a, z) => a === z,
     disabled = false,
     horizontal = false,
     multiple = false,
@@ -341,7 +343,14 @@ let ListboxRoot = forwardRefWithAs(function Listbox<
         value,
         onChange,
         mode: multiple ? ValueMode.Multi : ValueMode.Single,
-        compare: useEvent((a, z) => a === z),
+        compare: useEvent(
+          typeof by === 'string'
+            ? (a: TType, z: TType) => {
+                let property = by as unknown as keyof TType
+                return a[property] === z[property]
+              }
+            : by
+        ),
       },
     },
     labelRef: createRef(),
diff --git a/packages/@headlessui-react/src/components/radio-group/radio-group.test.tsx b/packages/@headlessui-react/src/components/radio-group/radio-group.test.tsx
index cf75a34..ca45345 100644
--- a/packages/@headlessui-react/src/components/radio-group/radio-group.test.tsx
+++ b/packages/@headlessui-react/src/components/radio-group/radio-group.test.tsx
@@ -322,7 +322,7 @@ describe('Rendering', () => {
     })
   )
 
-  describe.skip('Equality', () => {
+  describe('Equality', () => {
     let options = [
       { id: 1, name: 'Alice' },
       { id: 2, name: 'Bob' },
diff --git a/packages/@headlessui-react/src/components/radio-group/radio-group.tsx b/packages/@headlessui-react/src/components/radio-group/radio-group.tsx
index d668fb6..cd848b7 100644
--- a/packages/@headlessui-react/src/components/radio-group/radio-group.tsx
+++ b/packages/@headlessui-react/src/components/radio-group/radio-group.tsx
@@ -113,17 +113,25 @@ let RadioGroupRoot = forwardRefWithAs(function RadioGroup<
   props: Props<
     TTag,
     RadioGroupRenderPropArg,
-    RadioGroupPropsWeControl | 'value' | 'onChange' | 'disabled' | 'name'
+    RadioGroupPropsWeControl | 'value' | 'onChange' | 'disabled' | 'name' | 'by'
   > & {
     value: TType
     onChange(value: TType): void
+    by?: (keyof TType & string) | ((a: TType, z: TType) => boolean)
     disabled?: boolean
     name?: string
   },
   ref: Ref<HTMLElement>
 ) {
-  let { value, name, onChange, disabled = false, ...theirProps } = props
-  let compare = useEvent((a, z) => a === z)
+  let { value, name, onChange, by = (a, z) => a === z, disabled = false, ...theirProps } = props
+  let compare = useEvent(
+    typeof by === 'string'
+      ? (a: TType, z: TType) => {
+          let property = by as unknown as keyof TType
+          return a[property] === z[property]
+        }
+      : by
+  )
   let [state, dispatch] = useReducer(stateReducer, { options: [] } as StateDefinition<TType>)
   let options = state.options as unknown as Option<TType>[]
   let [labelledby, LabelProvider] = useLabels()
diff --git a/packages/@headlessui-react/src/utils/render.ts b/packages/@headlessui-react/src/utils/render.ts
index 6c942f6..36369ea 100644
--- a/packages/@headlessui-react/src/utils/render.ts
+++ b/packages/@headlessui-react/src/utils/render.ts
@@ -126,20 +126,20 @@ function _render<TTag extends ElementType, TSlot>(
   }
 
   let dataAttributes: Record<string, string> = {}
-  // if (slot) {
-  //   let exposeState = false
-  //   let states = []
-  //   for (let [k, v] of Object.entries(slot)) {
-  //     if (typeof v === 'boolean') {
-  //       exposeState = true
-  //     }
-  //     if (v === true) {
-  //       states.push(k)
-  //     }
-  //   }
-  //
-  //   if (exposeState) dataAttributes[`data-headlessui-state`] = states.join(' ')
-  // }
+  if (slot) {
+    let exposeState = false
+    let states = []
+    for (let [k, v] of Object.entries(slot)) {
+      if (typeof v === 'boolean') {
+        exposeState = true
+      }
+      if (v === true) {
+        states.push(k)
+      }
+    }
+
+    if (exposeState) dataAttributes[`data-headlessui-state`] = states.join(' ')
+  }
 
   if (Component === Fragment) {
     if (Object.keys(compact(rest)).length > 0) {
diff --git a/packages/@headlessui-vue/src/components/combobox/combobox.test.ts b/packages/@headlessui-vue/src/components/combobox/combobox.test.ts
index 50436cc..c579fb0 100644
--- a/packages/@headlessui-vue/src/components/combobox/combobox.test.ts
+++ b/packages/@headlessui-vue/src/components/combobox/combobox.test.ts
@@ -226,7 +226,7 @@ describe('Rendering', () => {
       })
     )
 
-    describe.skip('Equality', () => {
+    describe('Equality', () => {
       let options = [
         { id: 1, name: 'Alice' },
         { id: 2, name: 'Bob' },
diff --git a/packages/@headlessui-vue/src/components/combobox/combobox.ts b/packages/@headlessui-vue/src/components/combobox/combobox.ts
index e3ace3f..5e70ac2 100644
--- a/packages/@headlessui-vue/src/components/combobox/combobox.ts
+++ b/packages/@headlessui-vue/src/components/combobox/combobox.ts
@@ -35,6 +35,10 @@ import { useOutsideClick } from '../../hooks/use-outside-click'
 import { Hidden, Features as HiddenFeatures } from '../../internal/hidden'
 import { objectToFormEntries } from '../../utils/form'
 
+function defaultComparator<T>(a: T, z: T): boolean {
+  return a === z
+}
+
 enum ComboboxStates {
   Open,
   Closed,
@@ -112,6 +116,7 @@ export let Combobox = defineComponent({
   props: {
     as: { type: [Object, String], default: 'template' },
     disabled: { type: [Boolean], default: false },
+    by: { type: [String, Function], default: () => defaultComparator },
     modelValue: { type: [Object, String, Number, Boolean] },
     name: { type: String },
     nullable: { type: Boolean, default: false },
@@ -175,7 +180,11 @@ export let Combobox = defineComponent({
       value,
       mode,
       compare(a: any, z: any) {
-        return a === z
+        if (typeof props.by === 'string') {
+          let property = props.by as unknown as any
+          return a[property] === z[property]
+        }
+        return props.by(a, z)
       },
       nullable,
       inputRef,
@@ -458,7 +467,7 @@ export let Combobox = defineComponent({
         render({
           props: {
             ...attrs,
-            ...omit(incomingProps, ['nullable', 'multiple', 'onUpdate:modelValue']),
+            ...omit(incomingProps, ['nullable', 'multiple', 'onUpdate:modelValue', 'by']),
           },
           slot,
           slots,
diff --git a/packages/@headlessui-vue/src/components/listbox/listbox.test.tsx b/packages/@headlessui-vue/src/components/listbox/listbox.test.tsx
index 1766504..7fa2814 100644
--- a/packages/@headlessui-vue/src/components/listbox/listbox.test.tsx
+++ b/packages/@headlessui-vue/src/components/listbox/listbox.test.tsx
@@ -199,7 +199,7 @@ describe('Rendering', () => {
       })
     )
 
-    describe.skip('Equality', () => {
+    describe('Equality', () => {
       let options = [
         { id: 1, name: 'Alice' },
         { id: 2, name: 'Bob' },
diff --git a/packages/@headlessui-vue/src/components/listbox/listbox.ts b/packages/@headlessui-vue/src/components/listbox/listbox.ts
index 6d950c0..b3a123a 100644
--- a/packages/@headlessui-vue/src/components/listbox/listbox.ts
+++ b/packages/@headlessui-vue/src/components/listbox/listbox.ts
@@ -33,6 +33,10 @@ import { useOutsideClick } from '../../hooks/use-outside-click'
 import { Hidden, Features as HiddenFeatures } from '../../internal/hidden'
 import { objectToFormEntries } from '../../utils/form'
 
+function defaultComparator<T>(a: T, z: T): boolean {
+  return a === z
+}
+
 enum ListboxStates {
   Open,
   Closed,
@@ -112,6 +116,7 @@ export let Listbox = defineComponent({
   props: {
     as: { type: [Object, String], default: 'template' },
     disabled: { type: [Boolean], default: false },
+    by: { type: [String, Function], default: () => defaultComparator },
     horizontal: { type: [Boolean], default: false },
     modelValue: { type: [Object, String, Number, Boolean] },
     name: { type: String, optional: true },
@@ -167,7 +172,11 @@ export let Listbox = defineComponent({
       value,
       mode,
       compare(a: any, z: any) {
-        return a === z
+        if (typeof props.by === 'string') {
+          let property = props.by as unknown as any
+          return a[property] === z[property]
+        }
+        return props.by(a, z)
       },
       orientation: computed(() => (props.horizontal ? 'horizontal' : 'vertical')),
       labelRef,
@@ -337,7 +346,7 @@ export let Listbox = defineComponent({
         render({
           props: {
             ...attrs,
-            ...omit(incomingProps, ['onUpdate:modelValue', 'horizontal', 'multiple']),
+            ...omit(incomingProps, ['onUpdate:modelValue', 'horizontal', 'multiple', 'by']),
           },
           slot,
           slots,
diff --git a/packages/@headlessui-vue/src/components/radio-group/radio-group.test.ts b/packages/@headlessui-vue/src/components/radio-group/radio-group.test.ts
index 88365f6..e6aca27 100644
--- a/packages/@headlessui-vue/src/components/radio-group/radio-group.test.ts
+++ b/packages/@headlessui-vue/src/components/radio-group/radio-group.test.ts
@@ -505,7 +505,7 @@ describe('Rendering', () => {
     assertActiveElement(getByText('Option 3'))
   })
 
-  describe.skip('Equality', () => {
+  describe('Equality', () => {
     let options = [
       { id: 1, name: 'Alice' },
       { id: 2, name: 'Bob' },
diff --git a/packages/@headlessui-vue/src/components/radio-group/radio-group.ts b/packages/@headlessui-vue/src/components/radio-group/radio-group.ts
index 37a933a..8b4204c 100644
--- a/packages/@headlessui-vue/src/components/radio-group/radio-group.ts
+++ b/packages/@headlessui-vue/src/components/radio-group/radio-group.ts
@@ -27,6 +27,10 @@ import { Hidden, Features as HiddenFeatures } from '../../internal/hidden'
 import { attemptSubmit, objectToFormEntries } from '../../utils/form'
 import { getOwnerDocument } from '../../utils/owner'
 
+function defaultComparator<T>(a: T, z: T): boolean {
+  return a === z
+}
+
 interface Option {
   id: string
   element: Ref<HTMLElement | null>
@@ -71,6 +75,7 @@ export let RadioGroup = defineComponent({
   props: {
     as: { type: [Object, String], default: 'div' },
     disabled: { type: [Boolean], default: false },
+    by: { type: [String, Function], default: () => defaultComparator },
     modelValue: { type: [Object, String, Number, Boolean] },
     name: { type: String, optional: true },
   },
@@ -101,7 +106,11 @@ export let RadioGroup = defineComponent({
         )
       ),
       compare(a: any, z: any) {
-        return a === z
+        if (typeof props.by === 'string') {
+          let property = props.by as unknown as any
+          return a[property] === z[property]
+        }
+        return props.by(a, z)
       },
       change(nextValue: unknown) {
         if (props.disabled) return false
diff --git a/packages/@headlessui-vue/src/utils/render.ts b/packages/@headlessui-vue/src/utils/render.ts
index ce154ef..10c7426 100644
--- a/packages/@headlessui-vue/src/utils/render.ts
+++ b/packages/@headlessui-vue/src/utils/render.ts
@@ -86,20 +86,20 @@ function _render({
   let children = slots.default?.(slot)
 
   let dataAttributes: Record<string, string> = {}
-  // if (slot) {
-  //   let exposeState = false
-  //   let states = []
-  //   for (let [k, v] of Object.entries(slot)) {
-  //     if (typeof v === 'boolean') {
-  //       exposeState = true
-  //     }
-  //     if (v === true) {
-  //       states.push(k)
-  //     }
-  //   }
-  //
-  //   if (exposeState) dataAttributes[`data-headlessui-state`] = states.join(' ')
-  // }
+  if (slot) {
+    let exposeState = false
+    let states = []
+    for (let [k, v] of Object.entries(slot)) {
+      if (typeof v === 'boolean') {
+        exposeState = true
+      }
+      if (v === true) {
+        states.push(k)
+      }
+    }
+
+    if (exposeState) dataAttributes[`data-headlessui-state`] = states.join(' ')
+  }
 
   if (as === 'template') {
     if (Object.keys(incomingProps).length > 0 || Object.keys(attrs).length > 0) {