Current technological advancements have allowed robots to be successfully employed in the healthcare sector. However, the recently acquired ability of social robots to process social information and act according to it has potentially made them very well suited to support or conduct psychological interventions. The present paper carried out a systematic review of the available literature regarding social-robot-based interventions in psychological domains using preferred reporting items for systematic reviews and meta-analyses (PRISMA) guidelines. The inclusion criteria were: (i) publication date until 2020; (ii) being an empirical study, master thesis, or project report; (iii) written in English or Italian languages (the two languages spoken by the authors); (iv) published in a scholarly peer-reviewed journal or conference proceedings, or were Ph.D. or master’s theses; and (v) assessed “social robot”-based intervention in psychological domains. Overall, the review showed that three main areas may benefit from social-robot-based interventions: social skills, mood, and wellbeing (e.g., stress and anxiety levels). Interestingly, social robots seemed to have a performance comparable to, and sometimes even better than, human operators. The main, but not exclusive, target of robot-based interventions in the psychological field was children with autism spectrum disorder (ASD). As evidence is, however, still limited and in an embryonic state, deeper investigations are needed to assess the full potential of social robots for the purposes of psychological intervention. This is relevant, considering the role that social robots could have in overcoming barriers to access psychological assessment and therapies.