This thesis surveys and analyzes applications of machine learning techniques to the fields of animation and computer graphics. Data-driven techniques utilizing machine learning have in recent years been successfully applied to many subfields of animation and computer graphics. These include, but are not limited to, fluid dynamics, kinematics, and character modeling. I argue that such applications offer significant advantages which will be pivotal in advancing the fields of animation and computer graphics. Further, I argue these advantages are especially relevant in real-time implementations when working with finite computational resources.