LiDAR-based place recognition (LPR) technology processes 3D LiDAR point clouds and encodes them into feature descriptors, enabling mobile robots to recognize previously visited locations. This capability supports critical tasks such as loop closure detection and re-localization. With the rapid advancements in deep learning, deep learning-based LiDAR place recognition (DL-LPR) has emerged as the dominant research direction in this field. However, existing reviews on DL-LPR remain limited in scope. To address this gap, this paper focuses on DL-LPR, introducing its core concepts, system structures, and applications. It presents a coarse-to-fine classification framework to systematically categorize and review existing methods, based on two dimensions: input data structure and model architecture. Furthermore, this paper summarizes commonly used datasets and performance evaluation metrics, along with performance comparisons of representative methods. Finally, it provides an in-depth analysis of the challenges faced by DL-LPR in complex environments, such as long-term, large-scale, and dynamic settings, and offers insights into future development trends.