We describe recent work on CST, an online algorithm for constructing skill trees from demonstration trajectories. CST segments a demonstration trajectory into a chain of component skills, where each skill has a goal and is assigned a suitable abstraction from an abstraction library. These properties per- mit skills to be improved eciently using a policy learning algorithm. Chains from mul- tiple demonstration trajectories are merged into a skill tree. We describe applications of CST to acquiring skills from human demon- stration in a dynamic continuous domain and from both expert demonstration and learned control sequences on a mobile manipulator.