Multi-way communication is a means to significantly improve the spectral efficiency of wireless networks. This monograph provides an overview of the developments in this research area since it was initiated by Claude Shannon. The basic two-way communication channel is considered first, followed by the two-way relay channel obtained by the deployment of an additional cooperative relay node to improve the overall communication performance. This basic setup is then extended to multi-user systems. For all these setups, fundamental limits on the achievable rates are reviewed, making use of a...