As React applications become more complex, optimizing performance is crucial to prevent unnecessary re-renders, and React offers tools such as PureComponent for class components and React.memo for functional components to address this. PureComponent enhances performance by implementing shallow comparisons of state and props, thereby skipping re-renders if no changes are detected. Functional components, which cannot directly leverage PureComponent, can use React.memo to achieve similar optimization by wrapping the component to prevent updates unless props change. React.memo operates as a higher-order component and can be customized with a second argument to dictate specific re-render conditions. The shift towards functional components with Hooks, including React.memo, is recommended over class components for modern React development, promoting concise and efficient coding practices.