In this paper, we identify and discuss several groups of issues that arise in the design of interfaces for multiple users interacting with multiple devices. We analyze in what ways these interfaces differ from traditional single-user single device interfaces, and identify different characteristics of interfaces. We categorize a possible set of device types that may exist in an environment, and then discuss the fundamental issues that have to be addressed when designing multi-user multi-device interfaces. The focus is on user and device management, technical concerns and social concerns, and some of the topics discussed include coordination, assignment, sharing, load-limits, coverage, privacy concerns, and user alienation.