This article is a survey of deep learning methods for single and multiple sound source localization, with a focus on sound source localization in indoor environments, where reverberation and diffuse noise are present. We provide an extensive topography of the neural network-based sound source localization literature in this context, organized according to the neural network architecture, the type of input features, the output strategy (classification or regression), the types of data used for model training and evaluation, and the model training strategy. Tables summarizing the literature survey are provided at the end of the paper, allowing a quick search of methods with a given set of target characteristics.