Integration of deep learning in healthcare has revolutionized the analysis of complex, high-dimensional, and heterogeneous data. However, traditional single-modal approaches often fail to grasp the multi-faceted nature of human health, in which genetic, environmental, lifestyle, and physiological factors interact in complex ways. The rapid development of multimodal machine learning (MML) has been a transformational paradigm that allows seamless integration of these heterogeneous data sources toward a better understanding of health and disease. This review goes in-depth with the methodologies of MML, with special emphasis on the main strategies of fusion and advanced techniques. We also discuss the wide applications of MML in different health domains, such as brain disorders, cancer prediction, chest-related conditions, skin diseases, and other medical challenges. We illustrate, through detailed case studies, how MML provides better diagnostic accuracy, and personalized treatment strategies. While it has seen huge progress, MML is confronted with a few major challenges around data heterogeneity, alignment complexities, and the subtleties of effective fusion strategies. The review concludes with a discussion on the future directions calling for robust data integration techniques, efficient and scalable architectures, and fairness and bias mitigation. MML is still an evolving field, and it has the potential to revolutionize healthcare delivery and drive innovations in the direction of more personalized, equitable, and effective patient care globally.