We examine evidence for natural selection resulting in Apis mellifera becoming tolerant or resistant to Varroa mites in different bee populations. We discuss traits implicated in Varroa resistance and how they can be measured. We show that some of the measurements used are ambiguous, as they measure a combination of traits. In addition to behavioural traits, such as removal of infested pupae, grooming to remove mites from bees or larval odours, small colony size, frequent swarming, and smaller brood cell size may also help to reduce reproductive rates of Varroa. Finally, bees may be tolerant of high Varroa infections when they are resistant or tolerant to viruses implicated in colony collapse. We provide evidence that honeybees are an extremely outbreeding species. Mating structure is important for how natural selection operates. Evidence for successful natural selection of resistance traits against Varroa comes from South Africa and from Africanized honeybees in South America. Initially, Varroa was present in high densities and killed about 30% of the colonies, but soon after its spread, numbers per hive decreased and colonies survived without treatment. This shows that natural selection can result in resistance in large panmictic populations when a large proportion of the population survives the initial Varroa invasion. Natural selection in Europe and North America has not resulted in large-scale resistance. Upon arrival of Varroa, the frequency of traits to counter mites and associated viruses in European honey bees was low. This forced beekeepers to protect bees by chemical treatment, hampering natural selection. In a Swedish experiment on natural selection in an isolated mating population, only 7% of the colonies survived, resulting in strong inbreeding. Other experiments with untreated, surviving colonies failed because outbreeding counteracted the effects of selection. If loss of genetic variation is prevented, colony level selection in closed mating populations can proceed more easily, as natural selection is not counteracted by the dispersal of resistance genes. In large panmictic populations, selective breeding can be used to increase the level of resistance to a threshold level at which natural selection can be expected to take over.