The purpose of this paper is to present the most important achievements in the field of distribution power line inspection by mobile robots. Stimulated by the need for fast, accurate, safe and low-cost power line inspection, which would increase the quality of power delivery, the field of automated power line inspection has witnessed rapid development over the last decade. This paper addresses automated helicopter inspection, inspection with flying robots and inspection with climbing robots. The first attempts to automate power line inspection were conducted in the field of helicopter inspection. In recent years, however, the research was mostly focused on flying and climbing robots. These two types of robots for automated power line inspection are critically assessed according to four important characteristics: design requirements, inspection quality, autonomy and universality of inspection. Besides, some general not yet identified problems and tasks of inspection robots, which should be addressed in the future, are presented. In conclusion, the two robot types have specific benefits and drawbacks so that none can currently be considered generally advantageous.