This dissertation comprehensively studies diverse cooperative and noncooperative amplify-and-forward (AF) multiple-input multiple-output (MIMO) wireless relay networks. Various gain matrices and vectors, such as relay amplifying matrices and beamforming vectors, are determined by using diverse criterions, such as minimum mean square error (MMSE), maximum signal-to-noise ratio (SNR), zero-forcing (ZF), and achievable rate (AR). In addition, multiple power constraints are considered in the optimization problems during data transmission. Moreover, both certain and uncertain channel state information (CSI) are considered as well. In particular, both one- and two-way AF MIMO relay networks are studied. Furthermore, by adopting the derived optimum gain matrices and vectors, cost functions (CFs), total transmitted relay power, total signal component power (SCP) at the destinations, ARs, and equalizers at the destinations are compared to each other for different cases. In particular, the minimization MSE CF criterion for the efficient relay selection scheme is proposed in this dissertation. This work also shows the relationship between the mutual information (MI) in nats and the MMSE with unit power of the transmitted signal for one- and two-way AF relay networks. Finally, this dissertation verifies the analytical results through MMSE, bit error rate (BER), and AR simulations of both optimum one-way and two-way distributed AF wireless relay networks.