As one of the most versatile food crops, the potato (Solanum tuberosum) is used worldwide for human and animal consumption, and as raw material for starch and alcohol production. Nowadays, one of the most important aspects of potato production is tuber quality, that includes biological traits (e. g. proteins, carbohydrates, and minerals); sensorial traits (e.g. flavour, texture); and industrial traits (e.g. tuber shape, cold sweetening, starch quality). Since most quality traits are genetically controlled, breeding work can successfully meet the needs of a changing and demanding world. This article discusses some genetic and reproductive aspects that must be taken into account when breeding potato. It also highlights some breeding strategies that can be used to create novel genetic variability and to speed up the selection programs for quality traits. Exploitation of tuber-bearing Solanum species as source of valuable quality traits/allelic diversity the possibility to manipulate whole chromosome sets make sexual hybridization a powerful strategy to produce new valuable genotypes. Genetic engineering is an additional tool to produce new genetic variability and to study important metabolic pathways. Examples are given on the use of this strategy to produce starches with modified amylose to amylopectin ratio, and potatoes with a higher nutritional value. Finally, the potential of DNA markers for quality breeding based on marker-assisted selection is discussed.