Fairness, a criterion focuses on evaluating algorithm performance on different demographic groups, has gained attention in natural language processing, recommendation system and facial recognition. Since there are plenty of demographic attributes in medical image samples, it is important to understand the concepts of fairness, be acquainted with unfairness mitigation techniques, evaluate fairness degree of an algorithm and recognize challenges in fairness issues in medical image analysis (MedIA). In this paper, we first give a comprehensive and precise definition of fairness, following by introducing currently used techniques in fairness issues in MedIA. After that, we list public medical image datasets that contain demographic attributes for facilitating the fairness research and summarize current algorithms concerning fairness in MedIA. To help achieve a better understanding of fairness, and call attention to fairness related issues in MedIA, experiments are conducted comparing the difference between fairness and data imbalance, verifying the existence of unfairness in various MedIA tasks, especially in classification, segmentation and detection, and evaluating the effectiveness of unfairness mitigation algorithms. Finally, we conclude with opportunities and challenges in fairness in MedIA.