To manage the rumors in social media to reduce the harm of rumors in society. Many studies used methods of deep learning to detect rumors in open networks. To comprehensively sort out the research status of rumor detection from multiple perspectives, this paper analyzes the highly focused work from three perspectives: Feature Selection, Model Structure, and Research Methods. From the perspective of feature selection, we divide methods into content feature, social feature, and propagation structure feature of the rumors. Then, this work divides deep learning models of rumor detection into CNN, RNN, GNN, Transformer based on the model structure, which is convenient for comparison. Besides, this work summarizes 30 works into 7 rumor detection methods such as propagation trees, adversarial learning, cross-domain methods, multi-task learning, unsupervised and semi-supervised methods, based knowledge graph, and other methods for the first time. And compare the advantages of different methods to detect rumors. In addition, this review enumerate datasets available and discusses the potential issues and future work to help researchers advance the development of field.