Large language models (LLMs) have advanced medical reasoning, but static question-answering performance remains insufficient for clinical workflows that require evolving patient-state tracking, evidence integration, role coordination, and accountable decisions. LLM-based medical multi-agent systems (MAS) are being developed to move AI from isolated answer generation toward workflow-level clinical intelligence by combining role specialization, memory, tool use, retrieval, communication, and orchestration. This Review maps LLM-based medical MAS across diagnosis, treatment decision support, imaging, monitoring, surgery, hospital workflow automation, evidence synthesis, medical education, and safety governance. We further synthesize key architectures for collaboration, knowledge-augmented evidence chains, multimodal integration, privacy-preserving coordination, and adaptive optimization, together with evaluation strategies spanning outcomes, process quality, robustness, efficiency, human comparison, and temporal backtesting. We argue that medical MAS should be evaluated not as larger LLM workflows, but as clinical coordination infrastructures that redistribute evidence, responsibility, and risk across human-AI teams. Their value depends on auditable evidence chains, controllable orchestration, explicit role accountability, and clinician oversight, rather than autonomous answer generation. Before routine clinical use, future work should prioritize traceable evidence chains, human oversight, privacy-preserving collaboration, standardized reporting, regulatory readiness, and prospective clinical validation.