Book excerpt: This thesis deals with the Shannon-theoretic fundamental limits of channel coding for single-user channels with memory and feedback and for multi-user channels with side information. We first consider the feedback capacity of a class of symmetric channels with memory modelled as nite-state Markov channels. The symmetry yields the existence of a hidden Markov noise process that facilitates the channel description as a function of input and noise, where the function satisfies a desirable invertibility property. We show that feedback does not increase capacity for such class of finite-state channels and that both their non-feedback and feedback capacities are achieved by an independent and uniformly distributed input. As a result, the capacity is given as a difference of output and noise entropy rates, where the output is also a hidden Markov process; hence, capacity can be approximated via well known algorithms. We then consider the memoryless state-dependent multiple-access channel (MAC) where the encoders and the decoder are provided with various degrees of asymmetric noisy channel state information (CSI). For the case where the encoders observe causal, asymmetric noisy CSI and the decoder observes complete CSI, inner and outer bounds to the capacity region, which are tight for the sum-rate capacity, are provided. Next, single-letter characterizations for the channel capacity regions under each of the following settings are established: (a) the CSI at the encoders are non-causal and asymmetric deterministic functions of the CSI at the decoder (b) the encoders observe asymmetric noisy CSI with asymmetric delays and the decoder observes complete CSI; (c) a degraded message set scenario with asymmetric noisy CSI at the encoders and complete and/or noisy CSI at the decoder. Finally, we consider the above state-dependent MAC model and identify what is required to be provided to the receiver in order to get a tight converse for the sum-rate capacity. Inspired by the coding schemes of the lossless CEO problem as well as of a recently proposed achievable region, we provide an inner bound which demonstrates the rate required to transmit this information to the receiver.