Recent years have witnessed an explosive growth of mobile devices. Mobile devices are permeating every aspect of our daily lives. With the increasing usage of mobile devices and intelligent applications, there is a soaring demand for mobile applications with machine learning services. Inspired by the tremendous success achieved by deep learning in many machine learning tasks, it becomes a natural trend to push deep learning towards mobile applications. However, there exist many challenges to realize deep learning in mobile applications, including the contradiction between the miniature nature of mobile devices and the resource requirement of deep neural networks, the privacy and security concerns about individuals data, and so on. To resolve these challenges, during the past few years, great leaps have been made in this area. In this paper, we provide an overview of the current challenges and representative achievements about pushing deep learning on mobile devices from three aspects: training with mobile data, efficient inference on mobile devices, and applications of mobile deep learning. The former two aspects cover the primary tasks of deep learning. Then, we go through our two recent applications that apply the data collected by mobile devices to inferring mood disturbance and user identification. Finally, we conclude this paper with the discussion of the future of this area.