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Deep neural networks are becoming more and more popular due to their revolutionary success in diverse areas, such as computer vision, natural language processing, and speech recognition. However, the decision-making processes of these models are generally not interpretable to users. In various domains, such as healthcare, finance, or law, it is critical to know the reasons behind a decision made by an artificial intelligence system. Therefore, several directions for explaining neural models have recently been explored. In this thesis, I investigate two major directions for explaining deep neural networks. The first direction consists of feature-based post-hoc explanatory methods, that is, methods that aim to explain an already trained and fixed model (post-hoc), and that provide explanations in terms of input features, such as tokens for text and superpixels for images (feature-based). The second direction consists of self-explanatory neural models that generate natural language explanations, that is, models that have a built-in module that generates explanations for the predictions of the model.