As an essential problem in computer vision, salient object detection (SOD) has attracted an increasing amount of research attention over the years. Recent advances in SOD are predominantly led by deep learning-based solutions (named deep SOD). To enable in-depth understanding of deep SOD, in this paper, we provide a comprehensive survey covering various aspects, ranging from algorithm taxonomy to unsolved issues. In particular, we first review deep SOD algorithms from different perspectives, including network architecture, level of supervision, learning paradigm, and object-/instance-level detection. Following that, we summarize and analyze existing SOD datasets and evaluation metrics. Then, we benchmark a large group of representative SOD models, and provide detailed analyses of the comparison results. Moreover, we study the performance of SOD algorithms under different attribute settings, which has not been thoroughly explored previously, by constructing a novel SOD dataset with rich attribute annotations covering various salient object types, challenging factors, and scene categories. We further analyze, for the first time in the field, the robustness of SOD models to random input perturbations and adversarial attacks. We also look into the generalization and difficulty of existing SOD datasets. Finally, we discuss several open issues of SOD and outline future research directions. All the saliency prediction maps, our constructed dataset with annotations, and codes for evaluation are publicly available at https://github.com/wenguanwang/SODsurvey.