Mental illnesses, such as depression, are highly prevalent and have been shown to impact an individual's physical health. Recently, artificial intelligence (AI) methods have been introduced to assist mental health providers, including psychiatrists and psychologists, for decision-making based on patients' historical data (e.g., medical records, behavioral data, social media usage, etc.). Deep learning (DL), as one of the most recent generation of AI technologies, has demonstrated superior performance in many real-world applications ranging from computer vision to healthcare. The goal of this study is to review existing research on applications of DL algorithms in mental health outcome research. Specifically, we first briefly overview the state-of-the-art DL techniques. Then we review the literature relevant to DL applications in mental health outcomes. According to the application scenarios, we categorize these relevant articles into four groups: diagnosis and prognosis based on clinical data, analysis of genetics and genomics data for understanding mental health conditions, vocal and visual expression data analysis for disease detection, and estimation of risk of mental illness using social media data. Finally, we discuss challenges in using DL algorithms to improve our understanding of mental health conditions and suggest several promising directions for their applications in improving mental health diagnosis and treatment.