High prevalence of mental illness and the need for effective mental health care, combined with recent advances in AI, has led to an increase in explorations of how the field of machine learning (ML) can assist in the detection, diagnosis and treatment of mental health problems. ML techniques can potentially offer new routes for learning patterns of human behavior; identifying mental health symptoms and risk factors; developing predictions about disease progression; and personalizing and optimizing therapies. Despite the potential opportunities for using ML within mental health, this is an emerging research area, and the development of effective ML-enabled applications that are implementable in practice is bound up with an array of complex, interwoven challenges. Aiming to guide future research and identify new directions for advancing development in this important domain, this article presents an introduction to, and a systematic review of, current ML work regarding psycho-socially based mental health conditions from the computing and HCI literature. A quantitative synthesis and qualitative narrative review of 54 papers that were included in the analysis surfaced common trends, gaps, and challenges in this space. Discussing our findings, we (i) reflect on the current state-of-the-art of ML work for mental health, (ii) provide concrete suggestions for a stronger integration of human-centered and multidisciplinary approaches in research and development, and (iii) invite more consideration of the potentially far-reaching personal, social, and ethical implications that ML models and interventions can have, if they are to find widespread, successful adoption in real-world mental health contexts.