With the development of image-guided surgery and radiotherapy, the demand for medical image registration is stronger and the challenge is greater. In recent years, deep learning, especially deep convolution neural networks, has made excellent achievements in medical image processing, and its research in registration has developed rapidly. In this paper, the research progress of medical image registration based on deep learning at home and abroad is reviewed according to the category of technical methods, which include similarity measurement with an iterative optimization strategy, direct estimation of transform parameters, etc. Then, the challenge of deep learning in medical image registration is analyzed, and the possible solutions and open research are proposed.