Affective robotics research aims to better understand human social and emotional signals to improve human-robot interaction (HRI), and has been widely used during the last decade in multiple application fields. Past works have demonstrated, indeed, the potential of using affective robots (i.e., that can recognize, or interpret, or process, or simulate human affects) for healthcare applications, especially wellbeing. This paper systematically review the last decade (January 2013 - May 2022) of HRI literature to identify the main features of affective robotics for wellbeing. Specifically, we focused on the types of wellbeing goals affective robots addressed, their platforms, their shapes, their affective capabilities, and their autonomy in the surveyed studies. Based on this analysis, we list a set of recommendations that emerged, and we also present a research agenda to provide future directions to researchers in the field of affective robotics for wellbeing.