Robots will become part of our daily lives. As they do, they should not just be able to carry out specific tasks but also to partner with us socially and collaboratively. In addition, groups of robots could be interacting with groups of humans in joint activities. Yet, research related to groups of humans and robots is very limited. To make this happen we need a deeper understanding of how robots can interact socially in groups, how to identify and characterize other group members, evaluate the dependencies between the behaviours of different members; understand and consider different roles, and infer how the dynamics of group interactions led to a common past or build an anticipated future. In this talk I will discuss how to engineer social behaviours for robots that autonomously act as members of a group in multi-player games, played by both humans and social robots. I will start by providing an overview of recent work in social human-robot teams, and will present different scenarios to illustrate the work. I will address the issue of how humans respond to such social features in robots that convey different roles, such as partners, opponents, tutors or peers. Motivated by psychological research I will describe some studies conducted with our autonomous social robots and discuss results associated with trust, engagement, emotions and roles. I believe that by studying and engineering social interactions 'for' and 'with' robots in group settings, we will be building a new generation of natural, engaging, effective and, most importantly, 'humane' AI.