Growing interest in joint action, the ability to coordinate actions with others to bring about changes in the environment, has prompted questions about how individuals acting together take into account each other’s intentions, tasks, and actions. In this talk I will provide an overview of recent studies that have addressed these questions. Behavioural and electrophysiological experiments where pairs of participants performed tasks together showed that individual task performance changed as a function of the co-actor’s task even when this task was irrelevant for individual performance. These results indicate that people have a tendency to represent co-actors’ tasks and actions. New results on inter-group mimicry suggest that people acting together also form specific representations of actions to be performed jointly. I will discuss how these findings contribute to our understanding of the cognitive and neural mechanisms underlying joint action and consider implications for philosophical accounts of shared intentionality.