As robots advance from the pages and screens of science fiction into our homes, hospitals, and schools, they are poised to take on increasingly social roles. Consequently, the need to understand the mechanisms supporting humanmachine interactions is becoming increasingly pressing. We introduce a framework for studying the cognitive and brain mechanisms that support humanmachine interactions, leveraging advances made in cognitive neuroscience to link different levels of description with relevant theory and methods. We highlight unique features that make this endeavour particularly challenging (and rewarding) for brain and behavioural scientists. Overall, the framework offers a way to study the cognitive science of human-machine interactions that respects the diversity of social machines, individuals' expectations and experiences, and the structure and function of multiple cognitive and brain systems. From Social Cognition to Social Machines Over a decade ago, Microsoft founder Bill Gates prophesied a robotics revolution that would see staggering leaps in the progress and sophistication of robots, and predicted 'a robot in every home' in the near future [1]. Although the ubiquity of household robots has yet to be realised, we are opening our doors to an increasing number of artificially intelligent machines (see Glossary). Concurrently, a growing number of robotics start-ups are focusing on developing companion robots for the home or assistance robots to serve in complex, human-interactive contexts, including schools, hospitals, and care homes [2]. As progress towards developing machines that take on increasingly sophisticated social roles continues apace, the cognitive and brain mechanisms that underpin social engagement with these machines remain largely unknown. A greater understanding of the psychological and neurobiological foundations of human interactions with artificially intelligent social machines (henceforth referred to as 'social machines') has important implications for the design and programming of socially engaging and collaborative artificial agents. It is equally critical to use this understanding of human-machine interaction to further our knowledge of the flexibility and limits of neurocognitive processes supporting human social behaviour towards both human and artificial agents. Highlights Although machines designed to socially interact with humans are proliferating, our understanding of the mental processes supporting such interactions remains limited.