The combination of deep learning technology and adaptive optics technology is expected to effectively improve the wavefront correction effect and better cope with more complex environmental conditions. The research progress of applying deep learning in the direction of wavefront reconstruction and wavefront prediction is detailed, including the specific research methods and corresponding neural network structure design adopted by the researchers in these two research directions. The performance of these neural networks in different practical application scenarios is analyzed, the differences between different neural network structures are compared and discussed, and the specific impacts of the structural differences are explored. Finally, the existing methods of deep learning in these two directions are summarized, and the future development trend of the deep integration of deep learning and adaptive optics technology is also prospected.