In this paper, an analysis of the necessity to introduce classical function approximation theory and methods into the research of ANN is presented with a brief introduction of its contents. Then, the main results about the approximation capability of MLP network and the basic analysis methods are detailed from the two aspects of classical function appoximantion and statistical analysis. The approximation capability of RBF ntework is analyzed under the view of Regularity Theory, and the difference of the best approximation property between the RBF and MLP network is revealed.