The rise of non-linear and interactive media such as video games has increased the need for automatic movement animation generation. In this survey, we review and analyze different aspects of building automatic movement generation systems using machine learning techniques and motion capture data. We cover topics such as high-level movement characterization, training data, features representation, machine learning models, and evaluation methods. We conclude by presenting a discussion of the reviewed literature and outlining the research gaps and remaining challenges for future work. Machine Learning for Data-Driven Movement Generation: a Review of the State of the Art