In this paper, we present a taxonomy in Robot-Assisted Training; a growing body of research in Human-Robot Interaction which focuses on how robotic agents and devices can be used to enhance user's performance during a cognitive or physical training task. The proposed taxonomy includes a set of parameters that characterize such systems, in order to highlight the current research trends and needs for the design, development and evaluation of Robot-Assisted Training systems. Towards this direction, we review related taxonomies in Human Robot Interaction, as well as recent works and applications in Robot-Assisted Training. The motivation of this research is to identify and discuss issues and challenges, focusing on the personalization aspects of a Robot-Assisted Training system.