How do you implement animations within a custom widget?

Implementing animations in a custom widget involves using the 'AnimationController' and 'AnimationBuilder' classes. 'AnimationController' manages the animation's duration, forward, reverse, etc., while 'AnimationBuilder' is a widget that rebuilds when the animation changes. By combining these classes, developers can create smooth and dynamic animations within their widgets. The 'AnimatedContainer' and 'AnimatedWidget' are utility widgets that simplify the integration of animations into the widget tree. Understanding these concepts is crucial for creating visually appealing Flutter applications.