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The integration of Large Language Models (LLMs) into healthcare has catalyzed a significant technological leap, evolving from text-based Medical LLMs to Multimodal Medical LLMs (MLLMs) capable of interpreting complex clinical imaging. Despite these advancements, current models predominantly function as passive knowledge engines, proficient in answering queries but lacking the autonomy to navigate the dynamic, longitudinal nature of real-world patient care. This limitation has spurred a paradigm shift toward Medical Agents: proactive systems engineered to sense, reason, plan, and execute actions within clinical environments. In this survey, we provide a comprehensive roadmap of this evolutionary trajectory. We first review the foundational architectures and training strategies of state-of-the-art Medical LLMs and MLLMs. Subsequently, we formalize the construction of Medical Agentic Systems, distinguishing between the cognitive frameworks required for independent Single-Agent Systems and the collaborative paradigms of Multi-Agent Systems that simulate multidisciplinary clinical teams. Central to our analysis is the evolution of medical reasoning, which we categorize into three distinct stages: Core Reasoning for internal deliberation, Augmented Reasoning for tool-mediated and multimodal grounding, and Collective Reasoning for distributed medical intelligence. Finally, the survey examines the necessary transition in evaluation methodologies, from static benchmarks to interactive simulations, and discusses pressing open challenges, offering a forward-looking perspective on building reliable, safe, and clinically impactful medical AI. Project sources: https://github.com/ yczhou001/Awesome-Medical-LLM-Agent.