Fungal storage rots like blue mould, grey mould, bull’s eye rot, bitter rot and brown rot destroy large amounts of the harvested apple crop around the world. Application of fungicides is nowadays severely restricted in many countries and production systems, and these problems are therefore likely to increase. Considerable variation among apple cultivars in resistance/susceptibility has been reported, suggesting that efficient defence mechanisms can be selected for and used in plant breeding. These are, however, likely to vary between pathogens, since some fungi are mainly wound-mediated while others attack through lenticels or by infecting blossoms. Since mature fruits are considerably more susceptible than immature fruits, mechanisms involving fruit-ripening processes are likely to play an important role. Significant associations have been detected between the susceptibility to rots in harvested fruit and various fruit maturation-related traits like ripening time, fruit firmness at harvest and rate of fruit softening during storage, as well as fruit biochemical contents like acidity, sugars and polyphenols. Some sources of resistance to blue mould have been described, but more research is needed on the development of spore inoculation methods that produce reproducible data and can be used for large screenings, especially for lenticel-infecting fungi.