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Large AI models have demonstrated human-expert-level performance in specific medical domains. However, concerns regarding medical bias have prompted growing attention from the medicine, sociology, and computer science communities. Although research on medical bias in large AI models is rapidly expanding, efforts remain fragmented, often shaped by discipline-specific assumptions, terminology, and evaluation criteria. This survey provides a comprehensive synthesis of 55 representative studies, organizing the literature into three core themes: taxonomy of medical bias, methods for detection, and strategies for mitigation. Our analysis bridges the conceptual and methodological gaps across disciplines and highlights persistent challenges, including the lack of unified foundations for medical fairness, insufficient datasets and evaluation benchmarks, the lack of methods for rigorous automatic bias detection, missing real-world validation and continuous validation, inadequate representation, as well as insufficient studies on the trade-off between fairness and accuracy. Thereby, we identify and highlight emerging research opportunities to address these gaps. To further advance the field, we present a structured index of publicly available models and datasets referenced in these studies.