Humans easily recognize object parts and their hierarchical structure by watching how they move; they can then predict how each part moves in the future. In this paper, we propose a novel formulation that simultaneously learns a hierarchical, disentangled object representation and a dynamics model for object parts from unlabeled videos. Our Parts, Structure, and Dynamics (PSD) model learns to, first, recognize the object parts via a layered image representation; second, predict hierarchy via a structural descriptor that composes low-level concepts into a hierarchical structure; and third, model the system dynamics by predicting the future. Experiments on multiple real and synthetic datasets demonstrate that our PSD model works well on all three tasks: segmenting object parts, building their hierarchical structure, and capturing their motion distributions.