Amidst the fourth industrial revolution, social robots are resolutely moving from fiction to reality. With sophisticated artificial agents becoming ever more ubiquitous in daily life, researchers across different fields are grappling with the questions concerning how humans perceive and interact with these agents and the extent to which the human brain incorporates intelligent machines into our social milieu. This theme issue surveys and discusses the latest findings, current challenges and future directions in neuroscience- and psychology-inspired human–robot interaction (HRI). Critical questions are explored from a transdisciplinary perspective centred around four core topics in HRI: technical solutions for HRI, development and learning for HRI, robots as a tool to study social cognition, and moral and ethical implications of HRI. Integrating findings from diverse but complementary research fields, including social and cognitive neurosciences, psychology, artificial intelligence and robotics, the contributions showcase ways in which research from disciplines spanning biological sciences, social sciences and technology deepen our understanding of the potential and limits of robotic agents in human social life.