Learning by imitation is an essential process in human cognition. Recently, imitation learning has also become important in robotics research. We address the problem of learning by imitation in interactive, robotic agents using case-based reasoning. We describe two tasks for which case-based reasoning may be used: (i) interpretation, in which the robot interprets new skill demonstrations as being related to previous observations, and (ii) imitation, in which a robot seeks to use previously learned skills to address new problem scenarios. We present a case-based framework for imitation and interpretation in a robotic agent that learns from observations of a human teacher.