Mental health constitutes a complex and pervasive global challenge, affecting millions of lives and often leading to severe consequences. In this paper, we conduct a thorough survey to explore the intersection of data science, artificial intelligence, and mental healthcare, focusing on the recent developments of mental disorder detection through online social media (OSM). A significant portion of the population actively engages in OSM platforms, creating a vast repository of personal data that holds immense potential for mental health analytics. The paper navigates through traditional diagnostic methods, state-of-the-art data- and AI-driven research studies, and the emergence of explainable AI (XAI) models for mental healthcare. We review state-of-the-art machine learning methods, particularly those based on modern deep learning, while emphasising the need for explainability in healthcare AI models. The experimental design section provides insights into prevalent practices, including available datasets and evaluation approaches. We also identify key issues and challenges in the field and propose promising future research directions. As mental health decisions demand transparency, interpretability, and ethical considerations, this paper contributes to the ongoing discourse on advancing XAI in mental healthcare through social media. The comprehensive overview presented here aims to guide researchers, practitioners, and policymakers in developing the area of mental disorder detection.