This dissertation explores applications of machine learning for improving the quality of deformations in real-time character rigs as well as applications to assist artists in producing high-quality animations. We detail a deep learning-based approach to enable complex film-quality mesh deformations to run in real-time for both a character's body and face. Our method learns mesh deformations from an existing character rig and produces an accurate approximation using significantly less computational time. In addition to mesh deformations, we present a statistical approach to synthesize novel animations from a collection of artist-created animations. Thus, single-use animations for film can be leveraged for additional applications. We also present a method for generating facial animation from a recorded performance, which provides artists with an initial animation that can be fine-tuned to meet stylistic and expressive needs.