The surge in internet use to express personal thoughts and beliefs makes it increasingly feasible for the social NLP research community to find and validate associations between social media posts and mental health status . Cross-sectional and longitudinal studies of social media data bring to fore the importance of real-time responsible AI models for mental health analysis. Aiming to classify the research directions for social computing and tracking advances in the development of machine learning (ML) and deep learning (DL) based models, we propose a comprehensive survey on quantifying mental health on social media . We compose a taxonomy for mental healthcare and highlight recent attempts in examining social well-being with personal writings on social media. We define all the possible research directions for mental healthcare and investigate a thread of handling online social media data for stress, depression and suicide detection for this work. The key features of this manuscript are (i) feature extraction and classification, (ii) recent advancements in AI models, (iii) publicly available dataset, (iv) new frontiers and future research directions. We compile this information to introduce young research and academic practitioners with the field of computational intelligence for mental health analysis on social media. In this manuscript, we carry out a quantitative synthesis and a qualitative review with the corpus of over 92 potential research articles.