State dependent channels with state information at the transmitter, receiver, or both, have received much attention in recent years, due to the wide applicability of such models in communication systems. A common assumption in many of the works on this problem, is that the channel state is readily available, or at least can be accurately estimated, at the user's site. While this may be true in some cases, in many practical systems the state information is provided to the users by a third party. This is particularly true in network environments, where data on the channel state can be collected by part of the users, and then transmitted to all the active users in the network. In such a case, system resources—bandwidth, time slots, etc.—are allocated to this purpose. This raises the question of how to compress and distribute channel state information in those cases where the active users cannot measure the state directly. This chapter surveys known results on coding for state dependent channels, with constrained (i.e., rate-limited) and unconstrained side information. Starting from the basic result of Gel'fand & Pinsker, an overview is given on coding for state dependent broadcast and multiple access channels, and some recent results on coding for single and multiuser channels with compressed state information at the encoders.