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This monograph provides a tutorial review of the Lattice-Reduction-Aided and Integer-Forcing approaches to equalization in MIMO communications. The authors highlight the similarities and differences of both approaches while summarizing the various criteria for selecting the integer linear combinations available in the literature in a unified way. This presents the reader with a clear overview of the differing equalization techniques and enables them to be adopted for any particular system under development. The authors proceed to consider the demands on the signal constellations and coding schemes in detail. The monograph provides a concise overview of recent developments in the development of the widely-used MIMO communication systems. It is of interest to researchers, practitioners and students alike.