Vector detection techniques are necessary to suppress the crosstalk between transmission channels/users in a variety of different transmission schemes, e. g., DS-CDMA or BFDM. This thesis studies several vector detection techniques, which were designed with the goal to offer almost optimum performance at a computational complexity that is still tolerable for practical use. This includes a method known from operations research, namely Wolfe-s method. A major part of the thesis consists of an in-depth theoretical analysis of various types of discrete-time recurrent neural networks, improving and extending their existing theory in several points. The results from this theoretical analysis are applied to the special problem of vector detection, specifying several new vector detection techniques. To show the superiority of these schemes over conventional vector detection schemes, simulation results are given for different scenarios.