Humans can adapt existing movements and learn new movements when exposed to a changing body, diverse terrain, robotic interfaces, and other modifications to the person or the environment. In this talk, using a combination of mathematical models, simulations, and empirical evidence, I will describe the principles underlying locomotor adaptation and learning across timescales. At short timescales, humans respond via a robust default feedback controller that maintains stable locomotion, and at longer timescales humans slowly change this controller to optimize a performance metric, following a negative gradient estimated from intentional exploration. Our model predicts changes in symmetry, entrainment, and energy expenditure in multiple natural and human-machine interfacing tasks. I will also highlight ongoing work on understanding natural motor learning trajectories that unfold over the timescale of many months. Across tasks and timescales, I will highlight the inductive biases of an optimization-based modeling framework that are crucial to capture human motor learning phenomena.