“With the deep integration of artificial intelligence technology in the medical field, image analysis models based on deep learning have shown significant potential in multiple tasks. However, the performance of such models heavily relies on large-scale, high-quality training data, and medical data in real clinical environments often faces three major challenges: data scarcity, data heterogeneity, and data imbalance. Traditional deep learning models often exhibit overconfident and erroneous predictions when dealing with such complex data, and lack the ability to express cognitive uncertainty, posing potential safety threats to high-risk clinical decisions. Evidence based deep learning (EDL), as an emerging uncertainty quantification paradigm, models predictions based on evidence by introducing Dirichlet distributions into the output of neural networks. It can model accidental uncertainty and cognitive uncertainty to a certain extent, providing a powerful tool for dealing with real and complex medical data. This article systematically reviews the application of evidence deep learning in image analysis of complex medical data from the perspectives of data scarcity, data heterogeneity, and data imbalance. It elucidates the core advantages of evidence deep learning in utilizing unlabeled data, detecting abnormal samples, parsing and fusing conflicting evidence, identifying tail data, and arbitrating noisy data, thanks to its uncertainty quantification and inherent interpretability. The relevant algorithms mentioned in this article have been summarized at https://GitHub./oscrab/Medical EDL. Finally, this article summarizes the current challenges faced in this field and looks forward to future research directions, providing researchers with a clear roadmap to promote the construction of a safer, more reliable, and trustworthy next-generation intelligent medical imaging analysis system.”