MIMO systems using multiple transmitting and receiving antennas are by now well studied. Several axes of these schemes have been explored with the underlying MIMO channel assumed linear. However, when high-power amplifiers (HPA) operating near their peak efficiency operating points are employed in the communication chain, non-linear distortions are introduced in the transmitted signals, and the resulting MIMO channel will be non-linear. This book establishes the concept of Nonlinear MIMO communication channels. The book begins by examining the performance degradations caused by HPA nonlinearities in MIMO channels, using space-time codes and MIMO-beamforming systems as case studies. The book then concludes by highlighting some key HPA nonlinearity compensation techniques suitable for MIMO systems.