A survey of the state of the art in learning systems (automata and neural networks) which are of increasing importance in both theory and practice is presented. Learning systems are a response to engineering design problems arising from nonlinearities and uncertainty. Definitions and properties of learning systems are detailed. An analysis of the reinforcement schemes which are the heart of learning systems is given. Some results related to the asymptotic properties of the learning automata are presented as well as the learning systems models, and at the same time the controller (optimiser) and the controlled process (criterion to be optimised). Two learning schemes for neural networks synthesis are presented. Several applications of learning systems are also described.