Deep Learning (DL) has become a crucial technology for multimedia computing. It offers a powerful instrument to automatically produce high-level abstractions of complex multimedia data, which can be exploited in a number of applications, including object detection and recognition, speech-to- text, media retrieval, multimodal data analysis, and so on. The availability of affordable large-scale parallel processing architectures, and the sharing of effective open-source codes implementing the basic learning algorithms, caused a rapid diffusion of DL methodologies, bringing a number of new technologies and applications that outperform, in most cases, traditional machine learning technologies. In recent years, the possibility of implementing DL technologies on mobile devices has attracted significant attention. Thanks to this technology, portable devices may become smart objects capable of learning and acting. The path toward these exciting future scenarios, however, entangles a number of important research challenges. DL architectures and algorithms are hardly adapted to the storage and computation resources of a mobile device. Therefore, there is a need for new generations of mobile processors and chipsets, small footprint learning and inference algorithms, new models of collaborative and distributed processing, and a number of other fundamental building blocks. This survey reports the state of the art in this exciting research area, looking back to the evolution of neural networks, and arriving to the most recent results in terms of methodologies, technologies, and applications for mobile environments
