Radiology report generation (RRG) aims to automatically generate free-text descriptions from clinical radiographs, e.g., chest X-Ray images. RRG plays an essential role in promoting clinical automation and presents significant help to provide practical assistance for inexperienced doctors and alleviate radiologists' workloads. Therefore, consider these meaningful potentials, research on RRG is experiencing explosive growth in the past half-decade, especially with the rapid development of deep learning approaches. Existing studies perform RRG from the perspective of enhancing different modalities, provide insights on optimizing the report generation process with elaborated features from both visual and textual information, and further facilitate RRG with the cross-modal interactions among them. In this paper, we present a comprehensive review of deep learning-based RRG from various perspectives. Specifically, we firstly cover pivotal RRG approaches based on the task-specific features of radiographs, reports, and the cross-modal relations between them, and then illustrate the benchmark datasets conventionally used for this task with evaluation metrics, subsequently analyze the performance of different approaches and finally offer our summary on the challenges and the trends in future directions. Overall, the goal of this paper is to serve as a tool for understanding existing literature and inspiring potential valuable research in the field of RRG.