Advances in technology have seen mobile robots becoming a viable solution to many global challenges. A key limitation for tetherless operation, however, is the energy density of batteries. Whilst significant research is being undertaken into new battery technologies, wireless power transfer may be an alternative solution. The majority of the available technologies are not targeted toward the medium power requirements of mobile robots; they are either for low powers (a few Watts) or very large powers (kW). This paper reviews existing wireless power transfer technologies and their applications on mobile robots. The challenges of using these technologies on mobile robots include delivering the power required, system efficiency, human safety, transmission medium, and distance, all of which are analyzed for robots operating in a hazardous environment. The limitations of current wireless power technologies to meet the challenges for mobile robots are discussed and scenarios which current wireless power technologies can be used on mobile robots are presented.