The most important viral pathogens of the cultivated potato are Potato virus X (PVX) and Potato virus Y (PVY), which can reduce potato production up to 80%. Thus resistance breeding is one of the major goals of plant breeders. Wild potato species are good sources of resistance (R) genes. The resistant plants respond to viral infection with hypersensitive reaction (HR) or extreme resistance (ER). HR is accompanied by programmed cell death, while ER localizes the virus at the primary infection site and limits virus replication without visible symptoms. While HR is generally strain-specific, ER can act against a broad spectrum of viral pathogens. This review aims to describe the molecular mechanisms of resistance against PVX and PVY in potato.