Moving beyond the stimulus contained in observable agent behaviour, i.e. understanding the underlying intent of the observed agent is of immense interest in a variety of domains that involve collaborative and competitive scenarios, for example assistive robotics, computer games, robot-human interaction, decision support and intelligent tutoring. This review paper examines approaches for performing action recognition and prediction of intent from a multi-disciplinary perspective, in both single robot and multi-agent scenarios, and analyses the underlying challenges, focusing mainly on generative approaches.