Understanding and defining the meaning of "action" is substantial for robotics research. This becomes utterly evident when aiming at equipping autonomous robots with robust manipulation skills for action execution. Unfortunately, to this day we still lack both a clear understanding of the concept of an action and a set of established criteria that ultimately characterize an action. In this survey we thus first review existing ideas and theories on the notion and meaning of action. Subsequently we discuss the role of action in robotics and attempt to give a seminal definition of action in accordance with its use in robotics research. Given this definition we then introduce a taxonomy for categorizing action representations in robotics along various dimensions. Finally, we provide a systematic literature survey on action representations in robotics where we categorize relevant literature along our taxonomy. After discussing the current state of the art we conclude with an outlook towards promising research directions.