Extrinsic parameter calibration is the foundation and prerequisite for LiDAR and camera data fusion of the autonomous system. This technology is widely used in fields such as autonomous driving, mobile robots, intelligent surveillance, and visual measurement. The learning-based method is one of the targetless calibrating methods in LiDAR and camera calibration. Due to its advantages of fast speed, high accuracy, and robustness under complex conditions, it has gradually been applied in practice from a simple theoretical model in just a few years, becoming an indispensable and important method. This paper systematically summarizes the research and development of this type of method in recent years. According to the principle of calibration parameter estimation, learning-based calibration algorithms are divided into two categories: accurate calibrating estimation and relative calibrating prediction. The evolution routes and algorithm frameworks of these two types of algorithms are elaborated, and the methods used in the algorithms’ steps are summarized. The algorithm mechanism, advantages, limitations, and applicable scenarios are discussed. Finally, we make a summary, pointing out existing research issues and trends for future development.