The development of techniques for production of gynogenetic, androgenetic, polyploid, and monosex progenies in common carp (Cyprinus carpio L.) is described from a chronological perspective. Gynogenetic progenies were obtained either by suppression of the second meiotic division in eggs (meiotic gynogenesis) or by suppression of the first mitotic division in haploid embryos (mitotic gynogenesis). As a rule, gynogenetic progenies of common carp were all-female, revealing female homogamety (females—XX, males—XY) in this species. Induced gynogenesis results in increased homozygosity; the rate of increase depends on the type of gynogenesis. Inbreeding coefficient (F) for one generation of meiotic gynogenesis in common carp is about 0.6, while diploids obtained by mitotic gynogenesis are homozygous for all genes (F = 1.0). Mitotic gynogenesis was used for production of clones in common carp. In androgenetic progenies of common carp, YY males were identified, that after crossing with normal females (XX) produced all-male progenies. Triploids of common carp are characterized by a significant reduction in gonad development (especially ovaries). However, the reduction in gonad development did not result in an increase of somatic growth rate of fish. The procedure for androgen treatment to induce phenotypic sex reversal in genotypic females (XX) was elaborated. All-female progenies of common carp were produced on a large scale by crossing normal females (XX) with hormonally sex-reversed males (XX). Rearing of all-female progenies in conditions when fish normally reach sexual maturity before reaching of market size increased production yield by 7–8%. In a few cases distant hybridization resulted in polyploidy of fish without application of any physical treatment. The ability of hybrid females between crucian carp (Carassius auratus) and common carp to produce diploid (with unreduced chromosome number) gametes resulted in opportunities to produce triploid and tetraploid hybrid progenies.