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Since 1990 a substantial amount of research has been reported in the literature concerning the identification and control of nonlinear dynamical systems using artificial neural networks. Various methods for tracking based on inverse control have been proposed, and constitute one of the main thrusts of this research effort. A significant part of this work has been heuristic in nature, and the conclusions drawn are generally justified using computer simulations. The general success of the simulation studies has also resulted in the increased use of artificial neural networks as controllers in industrial applications. As a result, there is a real need for a better understanding of the questions and problems that can arise in such contexts. This paper attempts to provide the theoretical foundations as well as insights that are essential for the efficient design of neural network controllers based on inverse control.