The common carp is one of the main aquaculture species in the world. Despite this, most of the production is carried out using unselected strains. Selective breeding for fast growth has not proven to be effective in this species, but other traits (disease resistance, shape) could be successfully selected for. Most heritability estimates in the literature are unreliable due to environmental biases, but complementary results from population genetics and comparison of strains seem to indicate that there should be a potential for selective breeding in this species, including selection for growth rate, provided the base populations are variable enough (e.g. synthetic strains). New techniques such as parentage assignment with microsatellites and use of doubled haploid progenies may help describe much more accurately, without environmental bias, the genetic determination of traits of interest in the carp. This could be a new opportunity to design efficient breeding programs in this important species.