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As robots increasingly become part of our everyday lives, programming and interacting with them must become simpler and more natural. This article describes an approach for structuring and controlling complex robotic systems, focusing on humanoid robots, that uses imitation for interaction and learning. The approach is behavior-based and uses a small set of basis behaviors, or primitives, as the foundation for control. The notion of primitives is biologically inspired and combines perception and movement control: they are used for structuring and generating the humanoid's movements, and also serve for structuring and generating the humanoid's movements, and also serve to simplify classification of observed movements onto what is to be imitated. We demonstrate how the primitives serve to structure the imitation system, from perception of observed human movements, to classification into the primitive representation, to movement reconstruction. We validate these ideas with a 13 degrees-of-freedom physics-based humanoid simulation using visual data taken from aerobics, dancing, and athletics, and imitating the demonstrations.