Although running deep learning algorithms is challenging due to resource constraints on mobile and wearable devices, they provide performance improvements compared to lightweight or shallow architectures. The widespread application areas for ondevice deep learning include computer vision, image processing, natural language processing, and audio classification. However, mobile and wearable sensing applications are also gaining attention. They can benefit from on-device deep learning, given that these devices are integrated with various sensors and produce large amounts of data. This paper reviews state-of-the-art studies on on-device deep learning for mobile and wearable devices, particularly from the sensor data analytics perspective. We first discuss the general optimization techniques of deep learning algorithms to meet the resource limitations of the devices. Then, we elaborate on model update and personalization techniques and review the studies by classifying them according to several aspects, including application areas, sensors, types of devices, utilized DL algorithms, mode of implementation, methods for optimizing DL algorithms for the target devices, training method, implementation toolkit/platform, performance metrics and resource consumption analysis. Finally, we discuss the open issues and future research directions about on-device deep learning for mobile and wearable sensing applications.