In this article, we provide an overview of recent advances in computer-aided design techniques using neural networks for electromagnetic (EM) modeling and design applications. Summary of various recent neural network modeling techniques including passive component modeling, design and optimization using the models are discussed. Training data for the models are generated from EM simulations. The trained neural networks become fast and accurate models of EM structures. The models are then incorporated into various optimization methods and commercially available circuit simulators for fast design and optimization. We also provide an overview of recently developed neural network inverse modeling technique. Training a neural network inverse model directly may become difficult due to the nonuniqueness of the input-output relationship in the inverse model. Training data containing multivalued solutions are divided into groups according to derivative information. Multiple inverse submodels are built based on divided data groups and are then combined to form a complete model. Comparison between the conventional EMbased design approach and the inverse design approach has also been discussed. These computer-aided design techniques using neural models provide circuit level simulation speed with EM level accuracy avoiding the high computational cost of EM simulation.