Abstract <p>Robots are now successfully used for a wide range of tasks: conveyor assembly, warehouse logistics, movement along city streets, and indoor servicing. However, problems arise when using them in less structured and less prepared environments. Many of them appear in unmanned ground vehicles operations: during cargo delivery, rescue operations, animal observation, forest monitoring, field cultivation, scientific measurements, and military applications. Reliable and safe movement in open spaces, including rugged terrain, requires specialized approaches that take into account the limitations of onboard sensors, unsuitable ground, unstructured terrain, and the lack of special markings and terrain data, such as 3D or marked maps typical for urban or indoor operations. The purpose of this review was to examine algorithms and methods for localization and navigation of mobile robots used in modern systems for controlling autonomous movement over rough terrain in order to determine the current technical level, relevant scientific and technical problems, and the main areas of research aimed at solving them. This paper presents the results of a systematic review, including the characteristics of the problems under consideration, the sensory systems used in the methods, and the limitations of the methods. The main trends are outlined and a number of problems in the field of development of control systems for off-road robots are highlighted. The results of the review can be used to select a suitable control method for the available robot resources and the specifics of the task, as well as to identify promising research directions in this area.</p>