This thesis is concerned with the application of techniques that find the best broadband MIMO equaliser in terms of MSE or BER performance while keeping the computational cost as realistically low as possible. It examines established adaptive and analytic methods of doing this and then moves on to the application of subband adaptive filtering techniques to perform MIMO channel equalisation and detection, since this technique has been found to give considerable advantages with respect to computational complexity and convergence rate for related SISO applications. For many slow-converging low-cost adaptive algorithms applied to the inversion of channels, the convergence rate can be increased by use of subband processing, where, in independent frequency bands, separate smaller-scale adaptive algorithms are operated at a reduced update rate. We will apply such methods to the identification and inversion of MIMO channels. Fractionally spaced systems also are known to outperform their symbol-spaced counterparts hence these are factored into the subband MIMO systems developed. Many simulation results demonstrating the benefits of MIMO systems with respect to the channel capacity, the performance of various adaptive and analytic MIMO inversion techniques and the potential complexity and convergence rate improvements of the subband approach in the MIMO context are presented. Adaptation to MIMO systems generally take much longer than for SISO systems. For adaptive identification the time increases by an amount approximately equal to dimensions of the MIMO system.