Abstract Selective breeding for disease resistance utilises proven animal breeding methods to improve animal health, welfare and productivity. Unsurprisingly, it is receiving more and more attention from livestock breeders. However, there are a number of largely theoretical arguments that have been raised as potential problems in selection for disease resistance. These can be classified under sustainability, feasibility and desirability. This review considers each of these areas in turn. Several examples show that enhanced resistance to disease is stable under natural selection and therefore deliberate selection for disease resistance should also be stable and sustainable. The feasibility of selective breeding depends in part upon the heritability of the trait or traits used to measure disease resistance, as well as the amount of variation among animals. The heritability of traits associated with resistance to many important diseases is often high and considerable variation among animals exists. Consequently, selective breeding for enhanced disease resistance is certainly feasible. The desirability of breeding for disease resistance depends upon whether there are trade-offs with other economically important traits. By and large these remain to be defined. However, even if unfavourable associations exist, breeders can create selection indices that include traits with unfavourable associations and maximise the desired responses while attempting to minimise undesirable effects. In conclusion, so long as one or more diseases exert a significant influence on livestock production, selective breeding will be a useful tool to assist in disease control.