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Multiple input multiple output (MIMO) is an important technique of improving the spectral efficiency in wireless communications. In MIMO systems, it is usually required to jointly detect signals at the receiver. While the maximum likelihood (ML) MIMO detection provides an optimal performance with full receive diversity, its complexity grows exponentially with the number of transmit antennas. Thus, lattice reduction (LR) and list based detectors are developed to reduce the complexity. In this thesis, we first apply the partial maximum a posteriori probability (PMAP) principle to the list-based method for MIMO detection. It shows that the PMAP-based list detection outperforms the conventional list detection with a reasonably low complexity. To further improve the performance for slow fading MIMO channels, we develop the column reordering criteria (CRC) for the LR-based list detection. It shows that with our proposed CRC, the LR,-based list detection can provide a near ML performance with a sufficiently low complexity. Then, we develop a complexity efficient pre-voting cancellation based detection with pre-voting vector selection criteria for underdetermined MIMO systems and show that this scheme can exploit a near ML performance with full receive diversity. An extension of MIMO systems is multiuser MIMO systems, where the user selection becomes an effective way to increase diversity (multiuser diversity). If multiple users are selected to access the channel at a time, the selection problem becomes a combinatorial problem, where an exhaustive search may leads to highly computational complexity. Therefore, we propose a low complexity greedy user selection scheme with an iterative LR updating algorithm when a LR-based MIMO detector is used. It shows that the proposed selection scheme can provide a comparable performance to the combinatorial ones with much lower complexity.