The traditional visual SLAM systems take the monocular or stereo camera as input sensor, with complex map initialization and map point triangulation steps needed for 3D map reconstruction, which are easy to fail, computationally complex and can cause noisy measurements. The emergence of RGB-D camera which provides RGB image together with depth information breaks this situation. While a number of RGB-D SLAM systems have been proposed in recent years, the current classification research on RGB-D SLAM is very lacking, and their advantages and shortcomings remain unclear regarding different applications and perturbations, such as illumination transformation, noise and rolling shutter effect of sensors. In this paper, we mainly introduced the basic concept and structure of the RGB-D SLAM system, and then introduced the differences between the various RGB-D SLAM systems in the three aspects of tracking, mapping, and loop detection, and we make a classification study on different RGB-D SLAM algorithms according to the three aspect. Furthermore, we discuss some advanced topics and open problems of RGB-D SLAM, hoping that it will help for future exploring. In the end, we conducted a large number of evaluation experiments on multiple RGB-D SLAM systems, and analyzed their advantages and disadvantages, as well as performance differences in different application scenarios, and provided references for researchers and developers.