Multiple input multiple output (MIMO) systems are now a proven area in current and future telecommunications research. MIMO wireless channels, in which both the transmitter and receiver have multiple antennas, have been shown to provide high bandwidth efficiency. In this thesis, we cover MIMO communications technology with a focus on cellular systems and the MIMO broadcast channel (MIMO-BC). Our development of techniques and analysis for the MIMO-BC starts with a study of single user MIMO systems. One such single user technique is that of antenna selection. In this thesis, we discuss various flavours of antenna selection, with the focus on powerful, yet straightforward, norm-based algorithms. These algorithms are analyzed and the results of this analysis produce a powerful and flexible power scaling factor. This power scaling factor can be used to model the gains of norm-based antenna selection via a single signal-to-noise ratio (SNR)-based parameter. This provides a powerful tool for engineers interested in quickly seeing the effects of antenna selection on their systems. A novel low complexity power allocation scheme follows on from the selection algorithms. Named “Poor Man’s Waterfilling” (PMWF), this scheme can provide significant gains in low SNR systems with very little extra complexity compared to selection alone. We then compare a variety of algorithms for the MIMO-BC, ranging from selection to beamforming, to the optimal, yet complex, iterative waterfilling (ITWF) solution. In this thesis we show that certain algorithms perform better in different scenarios, based on whether there is shadow fading or not. A power scaling factor analysis is also performed on these systems. In the cases where the user’s link gains are widely varying, such as when shadowing and distance effects are present, user fairness is impaired when optimal and near optimal throughput occurs. This leads to a key problem in the MIMO-BC, the balance between user fairness and throughput performance. In an attempt to find a suitable balance between these two factors, we modify the ITWF algorithm by both introducing extra constraints and also by using a novel utility function approach. Both these methods prove to increase user fairness with only minor loss in throughput over the optimal systems. The introduction of MIMO systems to the cellular domain has been hampered by the effects of interference between the cells. In this thesis we move MIMO to the cellular domain, addressing the interference using two different methods. We first use power control, where the transmit power of the base station is controlled to optimize the overall system throughput. This leads to promising results using low complexity methods. Our second method is a novel method of collaboration between base stations. This collaboration transforms neighbouring cell sectors into macro-cells and this results in substantial increases in performance.