Mental health disorders such as bipolar disorder, anxiety, depression have become international challenges. Traditional diagnostic methods are often not objective, scalable, or sensitive to changes in the initial stages. This paper provides a survey of literature works aimed at the application of artificial intelligence, machine learning, deep learning, and their combinations for mental health analysis. Recent research in neuroimaging, speech signals, text data, as well as multimodal approaches, are reviewed to shed light on the potential such data modalities may hold in improving diagnostic accuracy and enabling personalized care. Some key findings include a proof of efficacy of structural neuroimaging for the assessment of biomarkers, of non-invasive diagnosis using EEG and audio-visual data, and the large language models role in the analysis of behavioral and textual data. This paper identifies gaps and provides insights into the strengths and limitations of applications of ML and DL in mental health research. The work aims to guide future research by outlining opportunities for scalable and effective AI-driven mental health diagnostics.