In the era of big data, where vast amounts of information are being generated and collected at an unprecedented rate, there is a pressing demand for innovative data-driven multi-modal fusion methods. These methods aim to integrate diverse neuroimaging perspectives to extract meaningful insights and attain a more comprehensive understanding of complex psychiatric disorders. However, analyzing each modality separately may only reveal partial insights or miss out on important correlations between different types of data. This is where data-driven multi-modal fusion techniques come into play. By combining information from multiple modalities in a synergistic manner, these methods enable us to uncover hidden patterns and relationships that would otherwise remain unnoticed. In this paper, we present an extensive overview of data-driven multimodal fusion approaches with or without prior information, with specific emphasis on canonical correlation analysis and independent component analysis. The applications of such fusion methods are wide-ranging and allow us to incorporate multiple factors such as genetics, environment, cognition, and treatment outcomes across various brain disorders. After summarizing the diverse neuropsychiatric magnetic resonance imaging fusion applications, we further discuss the emerging neuroimaging analyzing trends in big data, such as N-way multimodal fusion, deep learning approaches, and clinical translation. Overall, multimodal fusion emerges as an imperative approach providing valuable insights into the underlying neural basis of mental disorders, which can uncover subtle abnormalities or potential biomarkers that may benefit targeted treatments and personalized medical interventions.