Precision medicine increasingly depends on the joint interpretation of molecular, imaging, and longitudinal clinical information. Multimodal artificial intelligence (AI) offers a computational framework for integrating heterogeneous biomedical data, but performance gains reported in retrospective benchmarks do not automatically translate into clinical benefit. This comprehensive, PRISMA-informed narrative review critically synthesizes multimodal AI across multi-omics integration, radiology and computational pathology, electronic health records, foundation models, and generative AI. We compare early, intermediate, late, and attention-based fusion with respect to cross-modal interaction, robustness to missing modalities, interpretability, data requirements, and deployment feasibility. Recent quantitative studies are examined to distinguish internal benchmark performance from external and prospective validation. We further analyze domain shift, algorithmic bias, incomplete modalities, calibration, privacy, and regulatory translation, and summarize practical mitigation strategies. The emerging evidence indicates that multimodal models can improve risk stratification and treatment-response prediction when complementary modalities are genuinely informative; however, generalizability frequently declines across institutions, scanners, populations, and data-availability patterns. Future progress requires prospective evaluation, transparent reporting, subgroup analysis, clinically meaningful endpoints, uncertainty estimation, and lifecycle monitoring under evolving regulatory frameworks. A translational framework is proposed in which biological relevance, external validation, explainability, fairness, workflow integration, and clinical utility are treated as co-equal design objectives for trustworthy precision medicine.