Potato (Solanum tuberosum) is one of the most important food crops worldwide and yields of potato can be affected by virus infection. While more than 40 viruses have been found in potato, only nine viruses (potato leafroll virus, potato viruses A, M, S, V, X and Y, potato moptop virus and tobacco rattle virus) and one viroid (potato spindle tuber viroid) have a significant economic impact on potato, worldwide. This review describes the geographical distribution of the most important viruses infecting potato and the genes for resistance or tolerance that have been identified against these various infectious agents. In some cases such resistance genes have been found only in other Solanum species. Few genes for resistance to the vectors of these viruses have been obtained and even fewer have been deployed successfully. However, transgenic resistance in potato has been achieved against seven of these disease agents.