This paper describes the theory and the applications of artificial neural networks, especially in a control field. Artificial neural networks try to mimic the nerve system in a mammalian brain into a mathematical model. Therefore, neural networks have some desirable characteristics and capabilities similar to the brain system, such as parallel processing, learning, nonlinear mapping, and generalization. Recently, many researchers have developed neural networks as new tools in many fields such as pattern recognition, information processing, design, planning, diagnosis, and control. We survey hybrid systems of the neural networks, fuzzy sets, and Artificial Intelligence (AI) technologies. Fuzzy sets and technologies have been also implemented as new tools in many fields and shown to be useful. Therefore, we deal with the hybrid systems as key technologies in the future.