The emergence of virus variants able to circumvent the resistance mechanisms of host plants, i.e. resistance- ‐breaking variants, is a complex phenomenon that involves different evolutionary forces operating at different spatial scales. Resistance breakdown can be decomposed into three major steps: appearance of resistance- ‐breaking virus variants by mutation, accumulation of these variants in plants in competition with wild- ‐type viruses and spread from plant to plant. Resistance breakdown occurs when these three steps are achieved efficiently. If not, the resistance is said durable. Reverse genetics analyses allowed the identification of the mutational pathways responsible for resistance breakdown and the measure of fitness costs associated to these mutations in a number of resistance gene- ‐virus species pairs. However, predicting the consequences of these genetic parameters at higher scales (crop fields, heterogeneous agricultural landscapes) is far beyond our experimental capacities because of the high number of plant- ‐virus combinations to analyze and because of the high number of factors at play during virus emergences. For this purpose, we developed different mathematical models. An analytical model showed that the evolutionary constraint exerted on virus pathogenicity factors (the factors that are recognized by the plant resistance genes) was a good predictor of the durability of the corresponding plant resistance gene. In another approach, simulation models allowed quantifying the respective roles of genetic, demographic and epidemiological factors affecting viral populations during resistance breakdown and estimating what effects on resistance durability could be expected from different leverages available to plant breeders and growers (choice of resistance genes, distribution of resistant and susceptible cultivars among fields, additional control methods acting on epidemics).