Modern communication systems demand ever-increasing data rates. Meeting this increased demand is not easy due to regulation and fundamental physical constraints. The utilization of more than one antenna at both the transmitter and receiver produces a multiple-input multiple-output (MIMO) channel, thereby enabling (under certain channel conditions) increased data rates without the need for increased bandwidth or transmission power. Concurrent with this increase in bandwidth is an increase in the receiver's computational complexity which, for a brute-force detector, increases exponentially. For receivers that possess error correcting capabilities, the problem of constructing a detector with low computational complexity that allows for near-exact a posteriori detection is challenging for transmission schemes employing even a modest number of transmit antennas and modulation alphabet sizes. The focus of this dissertation is on the construction of MIMO detection algorithms with low and fixed computational complexity. Specifically, the detection algorithms in this dissertation generate a list of potential transmission vectors resulting in realizable communication receivers with low and fixed computational complexity combined with low error rate performance in both coded and uncoded systems. A key contribution in this dissertation is a breadth-first fixed-complexity algorithm known as the smart-ordered and candidate-adding algorithm that achieves a desirable performance-complexity tradeoff. This algorithm requires only a single pass of a search tree to find its list of transmission vectors. We then construct a framework within which we classify a large class of breadth-first detection algorithms. The design of receiver algorithms for MIMO systems employing space-time codes and error correction is an important area of study. In this dissertation we propose a low and fixed computational complexity algorithm for an increasingly significant algebraic space-time code known as the golden code. The notion of computational complexity is critical in the design of practical MIMO receivers. We provide an analysis of computational complexity in relation to list-based soft-output detection where, in some instances, bounds are placed on the computational complexity of MIMO detection. For this analysis we utilize a metric known as the number of branch metric computations. The value at which the log-likelihood ratio (LLR) of conditional probabilities for a transmitted bit being either a 1 or a 0 is 'clipped' has an impact on a system's error rate performance. We propose a new approach for determining LLR clipping levels that, in contrast to prior approaches which clip to a predetermined fixed LLR clipping level, exploits channel state information to improve the error rate performance of suboptimal detection algorithms. Orthogonal frequency-division (OFDM) multiplexing is an effective technique for combating frequency-selective wideband communication channels. It is common practice for MIMO-OFDM detectors to implement the same detector at each subcarrier, in which case the overall performance is dominated by the weakest subcarrier. We propose a hard-output list detection receiver strategy for MIMO-OFDM channels called nonuniform computational complexity allocation, whereby the receiver adapts the computational resources of the MIMO detector at each subcarrier to match a metric of the corresponding channel quality. The proposed nonuniform algorithm improves performance over uniform allocation.