In recent years, Adaptive Optics (AO) system is developing towards miniaturization and low cost. Because of its simple structure and wide application range, wavefront sensorless (WFSless) AO system has become a research hotspot in related fields. Under the condition that the hardware environment is determined, the system control algorithm determines the correction effect and convergence speed of WFSless AO system. The emerging deep learning and artificial neural network have injected new vitality into the control algorithms of WFSless AO system, and further promoted the theoretical and practical development of WFSless AO. On the basis of summarizing the previous control algorithms of WFSless AO system, the applications of convolution neural network (CNN), long-term memory neural network (LSTM) and deep reinforcement learning in WFSless AO system control in recent years are comprehensively introduced, and characteristics of various deep learning models in WFSless AO system are summarized. Applications of WFSless AO system in astronomical observation, microscopy, ophthalmoscopy, laser telecommunication and other fields are outlined.