Climbing robots are robotic systems to move over 2D or complex 3D environments such as walls, ceilings, roofs, and geometric structures and to conduct various tasks. They will not only replace human workers for carrying out risky tasks in hazardous environments, but also increase operational efficiency by eliminating the costly erection of scaffolding and staffing costs. Climbing robots have special characteristics and the ability to adhere to different types of 2D or 3D surfaces, move around, and carry appropriate tools and sensors to work, while self-sustaining their bodies. Therefore, the most significant criterion for designing a climbing robot is to equip it with an appropriate locomotive and adhesion mechanism for adapting to the given environmental requirements. In this paper, a classification of climbing robots and proper examples with a brief outline are presented with considerations of the locomotive and adhesion mechanisms. Also, a list of climbing robots is provided with respect to fields of application that range from cleaning tasks in the construction industry to human care systems in the biomedical service industry.