Gesture-based programming (GBP) is a paradigm for the evolutionary programming of dextrous robotic systems by human demonstration. We call the paradigm “gesture-based” because we try to capture, in real-time, the intention behind the demonstratrator's fleeting, context-dependent hand motions, contact conditions, finger poses, and even cryptic utterances, rather than just recording and replaying movement. The paradigm depends on a pre-existing knowledge base of capabilities, collectively called “encapsulated expertise”, that comprise the real-time sensorimotor primitives from which the run-time executable is constructed as well as providing the basis for interpreting the teacher's actions during programming. In this paper we first describe the GBP environment, which is not fully implemented. We then present a technique based on principal components analysis, augmentable with model-based information, for learing and recognizing sensorimotor primitives. This paper describes simple applications of the technique to a small mobile robot and a PUMA manipulator. The mobile robot learned to escape from jams while the manipulator learned guarded moves and rotational accommodation that are composable to allow flat plate mating operations. While these initial applications are simple, they demonstrate the ability to extract primitives from demonstration, recognize the learned primitives in subsequent demonstrations, and combine and transform primitives to create different capabilities, which are all critical to the GBP paradigm.