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Objective: Although aquaculture is the fastest sector in terms of animal protein production in the world, breeding programs in aquatic species have been delayed compared to livestock and plants. Breeding improvement programs in aquaculture are mainly based on using phenotypic and pedigree information in quantitative genetics. However, approaches based on genomic information such as marker assistant selection (MAS) and genomic selection (GS) have been used to improve economic traits in recent years. The present paper aimed to investigate the breeding principles in aquaculture from phenotypic selection to genomic selection, their advantages and limitations, and recent advances in different aquatic species. Results: Genomic selection increases genetic gain in aquaculture through increasing accuracy of selection, decreasing generation interval, decreasing inbreeding rate, better control of genetic and environmental interactions, and selection of animals with less sensitivity to environmental variation. Especially, genomic selection is suitable for difficult-to-measure or low heritability traits such as disease resistance, feed intake, reproduction traits, and carcass quality. Reference population size, marker density, mating design, number and size of families, and a number of generations are effective factors in the accuracy of genomic selection in aquaculture. Continuous advances in cost-effective technologies for genotyping especially genotyping-by-sequencing (GBS) and bioinformatics will facilitate the faster application of genomic selection in aquaculture. Conclusions: Although genomic selection has been used for about 20 aquatic species in recent years and has provided opportunities for the improvement of genetic gain. However, the advantages of this method should be evaluated in commercial and economic aquatic breeding programs. It is expected that genomic selection will be widely used in aquatic breeding in the future and pave the way for the sustainable development of this industry. [ABSTRACT FROM AUTHOR]