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Antenna spacing and the properties of a scattering environment can create correlation between channel coefficients. Temporal correlation between fading coefficients may also be present, because one may be unable or unwilling to fully interleave the channel symbols. This paper presents a comprehensive analysis of multiple-input multiple-output systems under correlated fading. We calculate pairwise-error-probability (PEP) expressions under quasi-static fading, fast fading, block fading, as well as arbitrarily temporally correlated fading, under Rayleigh and Rician conditions. We use the PEP expressions to calculate union bounds on the performance of trellis space-time codes, super orthogonal space-time codes, linear-dispersion codes, and diagonal algebraic space-time codes.