Efficient analysis and processing of dental images are crucial for dentists to achieve accurate diagnosis and optimal treatment planning. However, dental imaging inherently poses several challenges, such as low contrast, metallic artifacts, and variations in projection angles. Combined with the subjectivity arising from differences in clinicians' expertise, manual interpretation often proves time-consuming and prone to inconsistency. Artificial intelligence (AI)-based automated dental image analysis (DIA) offers a promising solution to these issues and has become an integral part of computer-aided dental diagnosis and treatment. Among various AI technologies, deep learning (DL) stands out as the most widely applied and influential approach due to its superior feature extraction and representation capabilities. To comprehensively summarize recent progress in this field, we focus on the two fundamental aspects of DL research-datasets and models. In this paper, we systematically review 260 studies on DL applications in DIA, including 49 papers on publicly available dental datasets and 211 papers on DL-based algorithms. We first introduce the basic concepts of dental imaging and summarize the characteristics and acquisition methods of existing datasets. Then, we present the foundational techniques of DL and categorize relevant models and algorithms according to different DIA tasks, analyzing their network architectures, optimization strategies, training methods, and performance. Furthermore, we summarize commonly used training and evaluation metrics in the DIA domain. Finally, we discuss the current challenges of existing research and outline potential future directions. We hope that this work provides a valuable and systematic reference for researchers in this field. All supplementary materials and detailed comparison tables will be made publicly available on GitHub.