The inference of 3D motion and dynamics of the human musculoskeletal system has traditionally been solved using physics-based methods that exploit physical parameters to provide realistic simulations. Yet, such methods suffer from computational complexity and reduced stability, hindering their use in computer graphics applications that require real-time performance. With the recent explosion of data capture (mocap, video) machine learning (ML) has started to become popular as it is able to create surrogate models harnessing the huge amount of data stemming from various sources, minimizing computational time (instead of resource usage), and most importantly, approximate real-time solutions. The main purpose of this paper is to provide a review and classification of the most recent works regarding motion prediction, motion synthesis as well as musculoskeletal dynamics estimation problems using ML techniques, in order to offer sufficient insight into the state-of-the-art and draw new research directions. While the study of motion may appear distinct to musculoskeletal dynamics, these application domains provide jointly the link for more natural computer graphics character animation, since ML-based musculoskeletal dynamics estimation enables modeling of more long-term, temporally evolving, ergonomic effects, while offering automated and fast solutions. Overall, our review offers an in-depth presentation and classification of ML applications in human motion analysis, unlike previous survey articles focusing on specific aspects of motion prediction.