Plant viruses are important agricultural pathogens, and are responsible for a significant number of commercially relevant plant diseases. There are very few efficient control measures for viral diseases, but the use of genetic resistance appears to be the most promising strategy, often conferring effective protection without additional costs or labour during the growing season, and without damaging the environment. Sources of virus resistance have been identified for most crop species, and many resistant cultivars are already commercially available and of widespread cultivation; however, much remains to be learned about genetic resistance. This review article considers three main aspects that require intense investigation. First, we review the identification of sources of resistance and how plant breeders and pathologists have focused on aspects of the breeding process particularly relevant to viruses, such as germplasm screening and the dissection of resistance phenotypes. Second, we review how molecular mechanisms controlling resistance have been unravelled, looking at case studies where resistance mechanisms are now understood in detail for each stage of the infection cycle. Third, we turn to the durability of resistance in a global context, examining factors that influence durability and how this can be predicted. We conclude with a short discussion of the technological and scientific opportunities provided by recent advances in the field