Heavy metals, the most potent contaminants of the environment, are discharged into the aquatic ecosystems through the effluents of several industries, resulting in serious aquatic pollution. This type of severe heavy metal contamination in aquaculture systems has attracted great attention throughout the world. These toxic heavy metals are transmitted into the food chain through their bioaccumulation in different tissues of aquatic species and have aroused serious public health concerns. Heavy metal toxicity negatively affects the growth, reproduction, and physiology of fish, which is threatening the sustainable development of the aquaculture sector. Recently, several techniques, such as adsorption, physio-biochemical, molecular, and phytoremediation mechanisms have been successfully applied to reduce the toxicants in the environment. Microorganisms, especially several bacterial species, play a key role in this bioremediation process. In this context, the present review summarizes the bioaccumulation of different heavy metals into fishes, their toxic effects, and possible bioremediation techniques to protect the fishes from heavy metal contamination. Additionally, this paper discusses existing strategies to bioremediate heavy metals from aquatic ecosystems and the scope of genetic and molecular approaches for the effective bioremediation of heavy metals.