This article is a survey on deep learning methods for single and multiple sound source localization. We are particularly interested in sound source localization in indoor/domestic environment, where reverberation and diffuse noise are present. We provide an exhaustive topography of the neural-based localization literature in this context, organized according to several aspects: 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. This way, an interested reader can easily comprehend the vast panorama of the deep learning-based sound source localization methods. Tables summarizing the literature survey are provided at the end of the paper for a quick search of methods with a given set of target characteristics.