SLAM is a modern technology of a simultaneous localization of a mobile robot in the environment of motion and mapping of the surrounding space. By using SLAM a robot determines its position (solves the problem of localization) in space and simultaneously builds a map of the environment. This is a major technology for approaching the problem of navigation of the mobile robots. Now certain algorithms are already available with the known solution for the problem of SLAM. SLAM algorithms are applied widely for control of the mobile devices moving on the roads or off roads, for control of the flying robots (autonomous robot planes, helicopters, dirigibles), and for control of the android walking robots. Of course, for each class of the mobile robots there are specific features of a concrete SLAM technology, but the main ideas remain the same. In the specified technology a robot orientates itself in relation to the known reference points, using the sensors providing information on the reference points. In the first SLAM algorithms video cameras and/or range finders were often used, and later satellite navigation sensors were used. The article presents a brief review of the popular effective solutions to the SLAM problem based on various sensor processing algorithms and using different hardware. Among them the basic SLAM methods, such as MonoSLAM, FastSLAM, VisualSLAM, INS-SLAM, and INS-GPS-SLAM are considered. Their description is presented in the same order as information about these methods appeared in literature, and in the specified row, so the subsequent methods are more improved, than the preceding ones. Now the above methods ensure a reliable navigation for the mobile robots, however, new methods appear, and research is going on, in particular, with the aim to increase the speed of the SLAM methods and develop new sensors providing information on the environment.