Neural computing is a very powerful class of modelling techniques capable of approximating extremely complex functional relationships. It has been increasingly used as a practical approach in such problems as pattern recognition, classification and function approximation. Within the broad range of different networks, the most widely used ones are the sigmoidal and the radial basis function ones. We discuss the use of these networks in function approximation problems, making emphasis on the network structures, training processes and learning algorithms. We give an overview of the most important theoretical developments in this field and outline the relevant practical open problems. Finally, we present our results on error bounds for function approximation by sigmoidal and radial basis function networks.