The integration of Artificial Emotional Intelligence (AEI) in robotic systems offers promising avenues for enhancing robot functioning and interactions with users. This chapter explores the design challenges and ethical dilemmas of creating “feeling machines”, examining whether robots can - or should - be equipped with emotions. Beginning with a brief overview of the role emotions play in human behaviour and cognition, the chapter addresses the feasibility of embedding emotions in social robots. Three main approaches are analysed: exploiting human tendency to anthropomorphise; simulating emotions on a superficial level for human–robot interactions (HRI); integrating a sort of emotional apparatus internal to the robot system. This leads to the much contested question: Can AI genuinely possess emotions? This discourse entails an examination of the different and sometimes conflicting theories of emotions, and the challenges of replicating human-like emotions in robots. The chapter further explores the possiblity that robots might develop non-human emotional states, necessitating new definitions and ethical paradigms.