Digital holographic microscopy (DHM) has attracted attention in the fields of biological imaging and materials science due to its advantages in high-precision quantitative phase imaging. However, the existence of conjugate images, the problem of phase wrapping, and the limited resolution have always hindered the wide application of DHM. In recent years, deep learning, as a specialized model for data feature extraction in machine learning, has been widely used in the field of optical imaging. In addition to improving imaging efficiency, its potential to solve imaging inverse problems has also been continuously explored by researchers, opening up a new path for the optical imaging. In this paper, we start from the working principle of deep learning applied to DHM, introduces its ideas and important mathematical concepts to solve the inverse problem of optical imaging, and at the same time summarizes the complete implementation process of deep learning. A brief summary of the research progress in recent years of deep learning in holographic reconstruction, auto-focusing and phase recovery, and holographic denoising and super-resolution is given, and summarize the existing problems in this research field and look forward to the development trend of research.