Abstract: A large amount of image data such as CT that needs storage and transmission is generated in medical research.It is hard for the hospital to handle all data of the numerous patients.Therefore,it is of vital impor-tance to compress these image data.Recently,learning-based medical image compression has become a new research trend with the development of artificial intelligence.Traditional methods in medical data compression are firstly reviewed.Further study in learning-based approaches is made,and the compression performance of these approaches in different medical image data such as brain CT and liver CT are shown.In the meantime,the advantages and disadvantages of these approaches in various aspects such as compression ratio,algorithm complexity and reconstruction quality are systematically summarized.It is pointed out that the combination of learning-based method and ROI-based method achieves high compression ratio brought by lossy compression,while keeping the feature information of the critical regions.Consequently,this approach is much more suit-able for medical image compression than others.Finally,the paper concluded with a discussion of future de-velopment in this field.