Aquaculture is the farming of aquatic organisms such as fish, crustaceans, molluscs, and aquatic plants. Selective breeding is a key tool used in aquaculture to improve the genetic makeup of farmed species and enhance their productivity and desirable traits. This review explores the application of quantitative genetic principles in fish breeding, which has advanced more slowly compared to livestock breeding. Traditional fish breeding designs are often complicated by confounding effects, making it necessary to modify standard practices to distinguish additive, maternal, and non-additive genetic influences for effective genetic improvement. Selective breeding is essential in aquaculture, offering rapid selection responses and significant genetic gains. Despite the economic importance of traits in aquaculture species, there is limited knowledge of their phenotypic and genetic parameters due to underdeveloped breeding programs. This review highlights various selective breeding programs for key species such as salmon, trout, tilapia, and carp. Carp breeding, crucial in Indian aquaculture, has demonstrated substantial growth rate enhancements through selective breeding. The review underscores the potential of selective breeding to enhance economically significant traits in aquaculture, emphasizing the need for ongoing research and development in genetic improvement strategies.