Digital twins are virtual replicas of physical entities and are poised to transform personalized medicine through the real-time simulation and prediction of human physiology. Translating this paradigm from engineering to biomedicine requires overcoming profound challenges, including anatomical variability, multi-scale biological processes, and the integration of multi-physics phenomena. This survey systematically reviews methodologies for building digital twins of human organs, structured around a pipeline decoupled into anatomical twinning (capturing patient-specific geometry and structure) and functional twinning (simulating multi-scale physiology from cellular to organ-level function). We categorize approaches both by organ-specific properties and by technical paradigm, with particular emphasis on multi-scale and multi-physics integration. A key focus is the role of artificial intelligence (AI), especially physics-informed AI, in enhancing model fidelity, scalability, and personalization. Furthermore, we discuss the critical challenges of clinical validation and translational pathways. This study not only charts a roadmap for overcoming current bottlenecks in single-organ twins but also outlines the promising, albeit ambitious, future of interconnected multi-organ digital twins for whole-body precision healthcare.