In this chapter system identification algorithms for sparse nonlinear multi input multi output (MIMO) systems are developed. These algorithms are potentially useful in a variety of application areas including digital transmission systems incorporating power amplifier(s) along with multiple antennas, cognitive processing, adaptive control of nonlinear multivariable systems, and multivariable biological systems. Sparsity is a key constraint imposed on the model. The presence of sparsity is often dictated by physical considerations as in wireless fading channelestimation. In other cases it appears as a pragmatic modelling approach that seeks to cope with the curse of dimensionality, particularly acute in nonlinear systems like Volterra type series.Three identification approaches are discussed: conventional identification based on both input and output samples, semi-blind identification placing emphasis on minimal input resources and blind identification whereby only output samples are available plus a-priori information on input characteristics. Based on this taxonomy a variety of algorithms, existing and new, are studied and evaluated by simulations.