With the rapid advancement of artificial intelligence and deep learning, medical image analysis has become a critical tool in modern healthcare, significantly improving diagnostic accuracy and efficiency. However, AI-based methods also raise serious privacy concerns, as medical images often contain highly sensitive patient information. This review offers a comprehensive overview of privacy-preserving techniques in medical image analysis, including encryption, differential privacy, homomorphic encryption, federated learning, and generative adversarial networks. We explore the application of these techniques across various medical image analysis tasks, such as diagnosis, pathology, and telemedicine. Notably, we organizes the review based on specific challenges and their corresponding solutions in different medical image analysis applications, so that technical applications are directly aligned with practical issues, addressing gaps in the current research landscape. Additionally, we discuss emerging trends, such as zero-knowledge proofs and secure multi-party computation, offering insights for future research. This review serves as a valuable resource for researchers and practitioners and can help advance privacy-preserving in medical image analysis.