Multi-modal medical image fusion (MMIF) is increasingly recognized as an essential technique for enhancing diagnostic precision and facilitating effective clinical decision-making within computer-aided diagnosis systems. MMIF combines data from X-ray, MRI, CT, PET, SPECT, and ultrasound to create detailed, clinically useful images of patient anatomy and pathology. These integrated representations significantly advance diagnostic accuracy, lesion detection, and segmentation. This comprehensive review meticulously surveys the evolution, methodologies, algorithms, current advancements, and clinical applications of MMIF. We present a critical comparative analysis of traditional fusion approaches, including pixel-, feature-, and decision-level methods, and delves into recent advancements driven by deep learning, generative models, and transformer-based architectures. A critical comparative analysis is presented between these conventional methods and contemporary techniques, highlighting differences in robustness, computational efficiency, and interpretability. The article addresses extensive clinical applications across oncology, neurology, and cardiology, demonstrating MMIF's vital role in precision medicine through improved patient-specific therapeutic outcomes. Moreover, the review thoroughly investigates the persistent challenges affecting MMIF's broad adoption, including issues related to data privacy, heterogeneity, computational complexity, interpretability of AI-driven algorithms, and integration within clinical workflows. It also identifies significant future research avenues, such as the integration of explainable AI, adoption of privacy-preserving federated learning frameworks, development of real-time fusion systems, and standardization efforts for regulatory compliance.