This paper introduces swarm user interfaces, a new class of human-computer interfaces comprised of many autonomous robots that handle both display and interaction. We describe the design of Zooids, an open-source open-hardware platform for developing tabletop swarm interfaces. The platform consists of a collection of custom-designed wheeled micro robots each 2.6 cm in diameter, a radio base-station, a high-speed DLP structured light projector for optical tracking, and a software framework for application development and control. We illustrate the potential of tabletop swarm user interfaces through a set of application scenarios developed with Zooids, and discuss general design considerations unique to swarm user interfaces.