A pair of salient tradeoffs have driven the multiple-input multiple-output (MIMO) systems developments. More explicitly, the early era of MIMO developments was predominantly motivated by the multiplexing-diversity tradeoff between the Bell Laboratories layered space-time and space-time block coding. Later, the linear dispersion code concept was introduced to strike a flexible tradeoff. The more recent MIMO system designs were motivated by the performance-complexity tradeoff, where the spatial modulation and space-time shift keying concepts eliminate the problem of inter-antenna interference and perform well with the aid of low-complexity linear receivers without imposing a substantial performance loss on generic maximum-likelihood/max a posteriori -aided MIMO detection. Against the background of the MIMO design tradeoffs in both uncoded and coded MIMO systems, in this treatise, we offer a comprehensive survey of MIMO detectors ranging from hard decision to soft decision. The soft-decision MIMO detectors play a pivotal role in approaching to the full-performance potential promised by the MIMO capacity theorem. In the near-capacity system design, the soft-decision MIMO detection dominates the total complexity, because all the MIMO signal combinations have to be examined, when both the channel's output signal and the a priori log-likelihood ratios gleaned from the channel decoder are taken into account. Against this background, we provide reduced-complexity design guidelines, which are conceived for a wide-range of soft-decision MIMO detectors.