The extent of economic damage to crop plants due to pests and diseases is very large and well documented. Minimizing this loss through the use of pesticides is expensive. The high cost of pesticides and the threat they pose to non-target organisms make breeding for disease resistance a cost-effective and attractive alternative. Seed for most annual crops, except potatoes, is still under 10% of the total production cost to the farm gate. Clearly, the returns from improvements in yield, quality, and resistance due to plant breeding are so great that public and private investment in this activity will grow. Disease resistance is thus a primary objective in every plant breeding program. For example, at the Plant Breeding Institute, of some 50 research staff who work with wheat, 16 are engaged solely on aspects of resistance to fungus diseases and aphids. National and local trials all over the world emphasize resistance in evaluating new cultivars. However, breeding for resistance has had many failures; the appearance of new races of old parasites and sometimes of new parasites has frequently caused the withdrawal of new and promising cultivars in almost every crop. In this paper we briefly review the major constraints to the use of disease resistance by breeders and farmers and discuss their consequences in terms of parasite evolution. Clearly, most plant breeders would like eventually to use genetic transformation to confer resistance on breeding lines. This is not yet possible, and the problem is to establish where and how to start this activity.