Single Image Deraining task aims at recovering the rain-free background from an image degraded by rain streaks and rain accumulation. For the powerful fitting ability of deep neural networks and massive training data, data-driven deep SID methods obtained significant improvement over traditional ones. Current SID methods usually focus on improving the deraining performance by proposing different kinds of deraining networks, while neglecting the interpretation of the solving process. As a result, the generalization ability may still be limited in real-world scenarios, and the deraining results also cannot effectively improve the performance of subsequent high-level tasks (e.g., object detection). To explore these issues, we in this paper re-examine the three important factors (i.e., data, rain model and network architecture) for the SID problem, and specifically analyze them by proposing new and more reasonable criteria (i.e., general vs. specific,synthetical vs. mathematical, black-box vs. white-box). We also study the relationship of the three factors from a new perspective of data, and reveal two different solving paradigms (explicit vs. implicit) for the SID task. We further discuss the current mainstream data-driven SID methods from five aspects, i.e., training strategy, network pipeline, domain knowledge, data preprocessing, and objective function, and some useful conclusions are summarized by statistics. Besides, we profoundly studied one of the three factors, i.e., data, and measured the performance of current methods on different datasets through extensive experiments to reveal the effectiveness of SID data. Finally, with the comprehensive review and in-depth analysis, we draw some valuable conclusions and suggestions for future research.