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Most human behaviors consist of multiple parts, steps, or subtasks. These structures guide our ac- tion planning and execution, but when we observe others, the latent structure of their actions is typ- ically unobservable, and must be inferred in order to learn new skills by demonstration, or to as- sist others in completing their tasks. For example, an assistant who has learned the subgoal struc- ture of a colleague’s task can more rapidly rec- ognize and support their actions as they unfold. Here we model how humans infer subgoals from observations of complex action sequences using a nonparametric Bayesian model, which assumes that observed actions are generated by approxi- mately rational planning over unknown subgoal sequences. We test this model with a behavioral experiment in which humans observed different se- ries of goal-directed actions, and inferred both the number and composition of the subgoal sequences associated with each goal. The Bayesian model predicts human subgoal inferences with high ac- curacy, and significantly better than several al- ternative models and straightforward heuristics. Motivated by this result, we simulate how learn- ing and inference of subgoals can improve perfor- mance in an artificial user assistance task. The Bayesian model learns the correct subgoals from fewer observations, and better assists users by more rapidly and accurately inferring the goal of their actions than alternative approaches.