diff --git a/packages/eslint-plugin-react-hooks/__tests__/ESLintRulesOfHooks-test.js b/packages/eslint-plugin-react-hooks/__tests__/ESLintRulesOfHooks-test.js
index 3314439cd35d5..662e9cc39b963 100644
--- a/packages/eslint-plugin-react-hooks/__tests__/ESLintRulesOfHooks-test.js
+++ b/packages/eslint-plugin-react-hooks/__tests__/ESLintRulesOfHooks-test.js
@@ -141,6 +141,46 @@ const tests = {
         return useHook1(useHook2());
       }
     `,
+    `
+      // Valid because hooks can be used in anonymous arrow-function arguments
+      // to forwardRef.
+      const FancyButton = React.forwardRef((props, ref) => {
+        useHook();
+        return <button {...props} ref={ref} />
+      });
+    `,
+    `
+      // Valid because hooks can be used in anonymous function arguments to
+      // forwardRef.
+      const FancyButton = React.forwardRef(function (props, ref) {
+        useHook();
+        return <button {...props} ref={ref} />
+      });
+    `,
+    `
+      // Valid because hooks can be used in anonymous function arguments to
+      // forwardRef.
+      const FancyButton = forwardRef(function (props, ref) {
+        useHook();
+        return <button {...props} ref={ref} />
+      });
+    `,
+    `
+      // Valid because hooks can be used in anonymous function arguments to
+      // React.memo.
+      const MemoizedFunction = React.memo(props => {
+        useHook();
+        return <button {...props} />
+      });
+    `,
+    `
+      // Valid because hooks can be used in anonymous function arguments to
+      // memo.
+      const MemoizedFunction = memo(function (props) {
+        useHook();
+        return <button {...props} />
+      });
+    `,
     `
       // Valid because classes can call functions.
       // We don't consider these to be hooks.
@@ -262,6 +302,24 @@ const tests = {
         });
       }
     `,
+    `
+      // This is valid because "use"-prefixed functions called in
+      // unnamed function arguments are not assumed to be hooks.
+      React.unknownFunction((foo, bar) => {
+        if (foo) {
+          useNotAHook(bar)
+        }
+      });
+    `,
+    `
+      // This is valid because "use"-prefixed functions called in
+      // unnamed function arguments are not assumed to be hooks.
+      unknownFunction(function(foo, bar) {
+        if (foo) {
+          useNotAHook(bar)
+        }
+      });
+    `,
     `
       // Regression test for incorrectly flagged valid code.
       function RegressionTest() {
@@ -437,6 +495,32 @@ const tests = {
       `,
       errors: [genericError('useHookInsideCallback')],
     },
+    {
+      code: `
+        // Invalid because it's a common misunderstanding.
+        // We *could* make it valid but the runtime error could be confusing.
+        const ComponentWithHookInsideCallback = React.forwardRef((props, ref) => {
+          useEffect(() => {
+            useHookInsideCallback();
+          });
+          return <button {...props} ref={ref} />
+        });
+      `,
+      errors: [genericError('useHookInsideCallback')],
+    },
+    {
+      code: `
+        // Invalid because it's a common misunderstanding.
+        // We *could* make it valid but the runtime error could be confusing.
+        const ComponentWithHookInsideCallback = React.memo(props => {
+          useEffect(() => {
+            useHookInsideCallback();
+          });
+          return <button {...props} />
+        });
+      `,
+      errors: [genericError('useHookInsideCallback')],
+    },
     {
       code: `
         // Invalid because it's a common misunderstanding.
@@ -695,6 +779,55 @@ const tests = {
         // conditionalError('useState'),
       ],
     },
+    {
+      code: `
+        // Invalid because it's dangerous and might not warn otherwise.
+        // This *must* be invalid.
+        const FancyButton = React.forwardRef((props, ref) => {
+          if (props.fancy) {
+            useCustomHook();
+          }
+          return <button ref={ref}>{props.children}</button>;
+        });
+      `,
+      errors: [conditionalError('useCustomHook')],
+    },
+    {
+      code: `
+        // Invalid because it's dangerous and might not warn otherwise.
+        // This *must* be invalid.
+        const FancyButton = forwardRef(function(props, ref) {
+          if (props.fancy) {
+            useCustomHook();
+          }
+          return <button ref={ref}>{props.children}</button>;
+        });
+      `,
+      errors: [conditionalError('useCustomHook')],
+    },
+    {
+      code: `
+        // Invalid because it's dangerous and might not warn otherwise.
+        // This *must* be invalid.
+        const MemoizedButton = memo(function(props) {
+          if (props.fancy) {
+            useCustomHook();
+          }
+          return <button>{props.children}</button>;
+        });
+      `,
+      errors: [conditionalError('useCustomHook')],
+    },
+    {
+      code: `
+        // This is invalid because "use"-prefixed functions used in named
+        // functions are assumed to be hooks.
+        React.unknownFunction(function notAComponent(foo, bar) {
+          useProbablyAHook(bar)
+        });
+      `,
+      errors: [functionError('useProbablyAHook', 'notAComponent')],
+    },
     {
       code: `
         // Invalid because it's dangerous.
diff --git a/packages/eslint-plugin-react-hooks/src/RulesOfHooks.js b/packages/eslint-plugin-react-hooks/src/RulesOfHooks.js
index 73636e60daf16..dbcc9c3de59bb 100644
--- a/packages/eslint-plugin-react-hooks/src/RulesOfHooks.js
+++ b/packages/eslint-plugin-react-hooks/src/RulesOfHooks.js
@@ -54,6 +54,41 @@ function isComponentName(node) {
   }
 }
 
+function isReactFunction(node, functionName) {
+  return (
+    node.name === functionName ||
+    (node.type === 'MemberExpression' &&
+      node.object.name === 'React' &&
+      node.property.name === functionName)
+  );
+}
+
+/**
+ * Checks if the node is a callback argument of forwardRef. This render function
+ * should follow the rules of hooks.
+ */
+
+function isForwardRefCallback(node) {
+  return !!(
+    node.parent &&
+    node.parent.callee &&
+    isReactFunction(node.parent.callee, 'forwardRef')
+  );
+}
+
+/**
+ * Checks if the node is a callback argument of React.memo. This anonymous
+ * functional component should follow the rules of hooks.
+ */
+
+function isMemoCallback(node) {
+  return !!(
+    node.parent &&
+    node.parent.callee &&
+    isReactFunction(node.parent.callee, 'memo')
+  );
+}
+
 function isInsideComponentOrHook(node) {
   while (node) {
     const functionName = getFunctionName(node);
@@ -62,6 +97,9 @@ function isInsideComponentOrHook(node) {
         return true;
       }
     }
+    if (isForwardRefCallback(node) || isMemoCallback(node)) {
+      return true;
+    }
     node = node.parent;
   }
   return false;
@@ -290,7 +328,8 @@ export default {
         // `undefined` then we know either that we have an anonymous function
         // expression or our code path is not in a function. In both cases we
         // will want to error since neither are React function components or
-        // hook functions.
+        // hook functions - unless it is an anonymous function argument to
+        // forwardRef or memo.
         const codePathFunctionName = getFunctionName(codePathNode);
 
         // This is a valid code path for React hooks if we are directly in a React
@@ -301,7 +340,7 @@ export default {
         const isDirectlyInsideComponentOrHook = codePathFunctionName
           ? isComponentName(codePathFunctionName) ||
             isHook(codePathFunctionName)
-          : false;
+          : isForwardRefCallback(codePathNode) || isMemoCallback(codePathNode);
 
         // Compute the earliest finalizer level using information from the
         // cache. We expect all reachable final segments to have a cache entry