Random searches are classified as either guided or unguided, depending on whether information is retained whenever the outcome of a trial step is learned. Furthermore, both the guided and unguided varieties of random search are given accelerated convergence by increasing the adopted step size in a successful search direction. Four representative examples of random search algorithms used for adaptive array applications are considered in this chapter: linear random search (LRS), accelerated random search (ARS), guided accelerated random search (GARS), and genetic algorithm (GA).