The increasing availability of large collections of electronic health record (EHR) data and unprecedented technical advances in deep learning (DL) have sparked a surge of research interest in developing DL based clinical decision support systems for diagnosis, prognosis, and treatment. Despite the recognition of the value of deep learning in healthcare, impediments to further adoption in real healthcare settings remain due to the black-box nature of DL. Therefore, there is an emerging need for interpretable DL, which allows end users to evaluate the model decision making to know whether to accept or reject predictions and recommendations before an action is taken. In this review, we focus on the interpretability of the DL models in healthcare. We start by introducing the methods for interpretability in depth and comprehensively as a methodological reference for future researchers or clinical practitioners in this field. Besides the methods' details, we also include a discussion of advantages and disadvantages of these methods and which scenarios each of them is suitable for, so that interested readers can know how to compare and choose among them for use. Moreover, we discuss how these methods, originally developed for solving general-domain problems, have been adapted and applied to healthcare problems and how they can help physicians better understand these data-driven technologies. Overall, we hope this survey can help researchers and practitioners in both artificial intelligence and clinical fields understand what methods we have for enhancing the interpretability of their DL models and choose the optimal one accordingly. This article is categorized under: Cancer > Computational Models.