Abstract A haploid is an organism that looks like a sporophyte, but has the chromosome complement of a reduced gamete. There are several ways in which haploids can occur or be induced in vivo: spontaneously, mostly associated with polyembryony, and through abnormal processes after crosses, like pseudogamy, semigamy, preferential elimination of the chromosomes of one parental species, and androgenesis. In the crops described, haploids are or are near to being used in basic research and plant breeding. The application of haploids in breeding self-pollinated crops is based on their potential for producing fully homozygous lines in one generation, which can be assessed directly in the field. Early generation testing of segregating populations is possible through haploids, because doubled haploids (DH) possess additive variance only. Haploids can also be applied in classical breeding programmes to make these more efficient through improved reliability of selection. The application of haploids in cross-pollinated crops is also based on a rapid production of DH-lines, which can be used as inbred lines for the production of hybrid varieties. By means of haploids all natural barriers to repeated selfing are bypassed. In autotetraploid crops there are two types of haploid. One cycle of haploidization leads to dihaploids; a second cycle produces monohaploids. The significance of dihaploids is in their greatly simplified genetics and breeding and in the possibility of estimation of the breeding value of tetraploid cultivars by assessing their dihaploids. The main drawback of dihaploids is their restriction to two alleles per locus. Also, after doubling, it is impossible to achieve tetra-allelism at many loci, the requirement for maximal performance of autotetraploid cultivars. Tetra-allelism can be obtained when improved dihaploids have a genetically controlled mechanism of forming highly heterozygous restitution gametes with the unreduced number of chromosomes. Monohaploids, after doubling or twice doubling, may lead to fully homozygous diploids and tetraploids. These are important for basic research, but not yet for practical application. Meiotic data of potato homozygotes at three ploidy levels are presented.