Multiple user channels with state information

State-dependent channels model communication scenarios where the underlying channel changes in time or space. Considerable research effort has been put forth in investigating properties of these channels when there is a single transmitter and a single receiver. The case in which the state information is available only at the transmitter has received special attention since it is the canonical model for other state information availability scenarios.; In this dissertation we consider state-dependent communication channels with many transmitters and many receivers. We investigate canonical examples of multiple user channels: the broadcast channel and the multiple access channel. We also consider the relay channel.; We consider two scenarios of state information availability at the transmitters: causal and noncausal knowledge of the state information. We present a complete characterization of the capacity region for the degraded broadcast channel when the state information is causally available at the transmitter. For the relay channel we establish upper and lower bounds on the capacity when the state information is causally available to the transmitter and the relay. We further show that the upper and lower bounds are tight when the relay channel is physically degraded. We give an achievable region for the multiple access channel when state information is causally available to the transmitters.; When the state information is noncausally available to the transmitters, we present achievable regions for multiple access channel, the degraded broadcast channel, and the relay channel. We then use these results to extend Costa's "writing on dirty paper" result to the Gaussian multiple access channel, the Gaussian broadcast channel, and the Gaussian degraded relay channel.