Artificial neural networks have been recognized as an important technique in microwave modeling and optimization. This paper gives an overview and recent developments on the knowledge based neural modeling techniques in microwave modeling and design. The knowledge based artificial neural networks are constructed by incorporating the existing knowledge such as empirical formulas, equivalent circuit models and semi-analytical equations in neural network structures. The existing knowledge reduces the complexity of neural network model. This combination requires less training data and has better extrapolation performance than classical neural networks. The advantages of using knowledge based neural network modeling are demonstrated with two microwave modeling applications such as characteristic impedance modeling of thin-film microstrip line and parametric modeling of the differential via holes. (C) 2010 Published by Elsevier Ltd.