Potato virus Y (PVY) is the most economically important virus affecting potato production. PVY manipulates the plant cell machinery in order to successfully complete the infecting cycle. On the other side, the plant activates a sophisticated multilayer immune defense response to combat viral infection. The balance between these mechanisms, depending on the plant genotype and environment, results in a specific outcome that can be resistance, sensitivity, or tolerance. In this review, we summarize and compare the current knowledge on molecular events, leading to different phenotypic outcomes in response to PVY and try to link them with the known molecular mechanisms.