Mental health plays a key role in everyone’s day-to-day lives, impacting our thoughts, behaviours, and emotions. Also, over the past years, given its ubiquitous and affordable characteristics, the use of smartphones and wearable devices has grown rapidly and provided support within all aspects of mental health research and care, spanning from screening and diagnosis to treatment and monitoring, and attained significant progress to improve remote mental health interventions. While there are still many challenges to be tackled in this emerging cross-discipline research field, such as data scarcity, lack of personalisation, and privacy concerns, it is of primary importance that innovative signal processing and deep learning techniques are exploited. Particularly, recent advances in deep learning can help provide the key enabling technology for the development of the next-generation user-centric mobile mental health applications. In this article, we first brief basic principles associated with mobile device-based mental health analysis, review the main system components, and highlight conventional technologies involved. Next, we describe several major challenges and various deep learning technologies that have potentials for a strong contribution in dealing with these challenges, respectively. Finally, we discuss other remaining problems which need to be addressed via research collaboration across multiple disciplines.