Understanding the dynamical processes that govern the performance of functional materials is essential for the design of next generation materials to tackle global energy and environmental challenges. Many of these processes involve the dynamics of individual atoms or small molecules in condensed phases, e.g. lithium ions in electrolytes, water molecules in membranes, molten atoms at interfaces, etc., which are difficult to understand due to the complexity of local environments. In this work, we develop graph dynamical networks, an unsupervised learning approach for understanding atomic scale dynamics in arbitrary phases and environments from molecular dynamics simulations. We show that important dynamical information, which would be difficult to obtain otherwise, can be learned for various multi-component amorphous material systems. With the large amounts of molecular dynamics data generated every day in nearly every aspect of materials design, this approach provides a broadly applicable, automated tool to understand atomic scale dynamics in material systems.