Inverse modeling of microwave components plays an important role in microwave design and diagnosis or tuning. Since the analytical function or formula of the inverse input-output relationship does not exist and is difficult to obtain, artificial neural network (ANN) becomes an efficient tool to develop inverse models for microwave components. This paper provides an overview of recent advances in neural network-based inverse modeling techniques for microwave applications. We review two different shallow neural network-based inverse modeling techniques, including the comprehensive neural network inverse modeling methodology and the multivalued neural network inverse modeling technique. Both techniques address the problem of nonuniqueness in inverse modeling. We also provide an overview of recently developed hybrid deep neural network modeling technique and the application to inverse modeling. For the inverse modeling problem with high-dimensional inputs, the relationship between the inputs and the outputs of the inverse model will become more complicated and the inverse modeling problem will become harder. The deep neural network becomes a practical choice. The hybrid deep neural network structure is presented. The recently proposed activation function, specifically for microwave application, and a three-stage deep learning algorithm for training the hybrid deep neural network are reviewed. K E Y W O R D S artificial neural network, deep learning, deep neural network, inverse modeling, microwave components