While general-purpose large language models (LLMs) demonstrate remarkable capabilities, their clinical application demands rigorous adaptation to ensure safety and accuracy. This review presents a comprehensive framework for transforming LLMs into trustworthy medical specialists. We detail three core knowledge-injection strategies-(1) static embedding to internalize foundational biomedical knowledge; (2) behavioral alignment to enforce clinical safety and verifiable diagnostic logic; and (3) dynamic injection, such as retrieval-augmented generation, for real-time evidence grounding-together with multimodal integration as a complementary perception-injection paradigm extending the input space beyond text to imaging, biosignals, and tabular data. Building on these strategies, we further explore the evolution toward agentic AI systems that orchestrate them for autonomous, collaborative clinical decision-making. Finally, we discuss critical challenges, including model calibration, resource constraints, standardized reporting, and robust safety protocols. Combining these complementary strategies is essential for developing deployable, domain-specialized clinical AI systems.