Global warming and human-induced eutrophication drive the occurrence of various cyanotoxins in aquatic environments. These metabolites reveal diversified mechanisms of action, encompassing cyto-, neuro-, hepato-, nephro-, and neurotoxicity, and pose a threat to aquatic biota and human health. In the present paper, we review data on the occurrence of the most studied cyanotoxins, microcystins, nodularins, cylindrospermopsin, anatoxins, and saxitoxins, in the aquatic environment, as well as their potential bioaccumulation and toxicity in fish. Microcystins are the most studied among all known cyanotoxins, although other toxic cyanobacterial metabolites are also commonly identified in aquatic environments and can reveal high toxicity in fish. Except for primary toxicity signs, cyanotoxins adversely affect the antioxidant system and anti-/pro-oxidant balance. Cyanotoxins also negatively impact the mitochondrial and endoplasmic reticulum by increasing intracellular reactive oxygen species. Furthermore, fish exposed to microcystins and cylindrospermopsin exhibit various immunomodulatory, inflammatory, and endocrine responses. Even though cyanotoxins exert a complex pressure on fish, numerous aspects are yet to be the subject of in-depth investigation. Metabolites other than microcystins should be studied more thoroughly to understand the long-term effects in fish and provide a robust background for monitoring and management actions.