Abstract : Multiple-input multiple-output (MIMO) Volterra models have applications in different areas, including telecommunications. An overview of the modeling of nonlinear communication channels using MIMO Volterra models is presented in this paper. First, the development of an equivalent baseband discrete-time representation of a single-input single-output (SISO) Volterra system is carried out. This development constitutes the basis for several versions of discrete-time equivalent baseband MIMO Volterra systems presented in the sequel. The spectral broadening provided by a Volterra system on the equivalent baseband received signals is shown by calculating the frequency domain representation of the Volterra channel output. Some important block structured nonlinear MIMO models are also described, with their link to MIMO Volterra models. Finally, some applications of such models for communication systems are briefly discussed.