The last few years have seen significant progress in our understanding of how one should structure multi-robot systems. New control, coordination, and communication strategies have emerged and in this talk, we summarize some of these developments. In particular, we will discuss how to go from local rules to global behaviors in a systematic manner in order to achieve distributed geometric objectives, such as achieving and maintaining formations, area coverage, and swarming behaviors. We will also investigate how users can interact with networks of mobile robots in order to inject new information and objectives. The efficacy of these interactions depends directly on the interaction dynamics and the structure of the underlying information-exchange network. We will relate these network-level characteristics to controllability and manipulability notions in order to produce effective human-swarm interaction strategies.