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Skin cancer is one of the most threatening diseases worldwide. However, diagnosing skin cancer correctly is challenging. Recently, deep learning algorithms have emerged to achieve excellent performance on various tasks. Particularly, they have been applied to the skin disease diagnosis tasks. In this paper, we present a review on deep learning methods and their applications in skin disease diagnosis. We first present a brief introduction to skin diseases and image acquisition methods in dermatology, and list several publicly available skin datasets for training and testing algorithms. Then, we introduce the conception of deep learning and review popular deep learning architectures. Thereafter, popular deep learning frameworks facilitating the implementation of deep learning algorithms and performance evaluation metrics are presented. As an important part of this article, we then review the literature involving deep learning methods for skin disease diagnosis from several aspects according to the specific tasks. Additionally, we discuss the challenges faced in the area and suggest possible future research directions. The major purpose of this article is to provide a conceptual and systematically review of the recent works on skin disease diagnosis with deep learning. Given the popularity of deep learning, there remains great challenges in the area, as well as opportunities that we can explore in the future.