In recent years, the demand for reliable transmission of high speed data and multimedia traffic in wireless communications has been growing tremendously. To enhance the capacity of the existing and future generation wireless systems, attention has been recently turned into Smart Antenna (SA) and Multiple Input Multiple Output (MIMO) systems which may use adaptive beamforming. This dissertation aims at investigating and designing beamforming algorithms for multiple antenna wireless communication systems. In the first part of the dissertation, the system level performance of the Universal Mobile Telecommunication System (UMTS) with SAs at the Base Stations (BSs) is evaluated by using a novel and dynamic system level simulator. Compared with other investigations, the present evaluation takes into account the dynamic and stochastic behaviour of the radio propagation channel along with power control, soft handover and code management. The second part of the dissertation is devoted to downlink beamforming based on uplink channel parameters for UMTS Frequency Division Duplex (FDD) systems. A robust transformation of uplink to downlink spatial covariance matrices is proposed in order to overcome the adverse effect of uplink channel estimation errors into downlink beamforming. This method performs better than the previous approaches and can be efficiently implemented for realistic wireless networks. Robust uplink and downlink beamforming algorithms based on an outage probability criterion have been proposed in the third part of the dissertation. These algorithms reduce the degradation in system level performance caused by the uncertainty of the uplink and downlink spatial covariance matrices. Compared with the earlier robust methods based on worst-case performance optimization, the proposed algorithms do not need the knowledge of the upper bound of the uncertainty. In the last part of this dissertation, a new stochastic approach is proposed for the design of a single user robust MIMO transmitter which has only partial Channel State Information (CSI). The proposed transmitter enhances the robustness of the MIMO system against erroneous CSI. A power control optimization problem for multiuser MIMO system is also solved in order to minimize the BS transmit power while maintaining a minimum level of Quality of Service (QoS) for all Mobile Stations (MSs).