The use of fish in scientific research is increasing worldwide, due to both the rapid expansion of the fish farming industry and growing awareness of questions concerning the humane use of mammalian models in basic research and chemical testing. As fish are lower on the evolutionary scale than mammals, they are considered to be less sentient. Fish models are providing researchers, and those concerned with animal welfare, with opportunities for adhering to the Three Rs principles of refinement, reduction and replacement. However, it should be kept in mind that fish should also be covered by the principles of the Three Rs. Indeed, various studies have shown that fish are capable of nociception, and of experiencing pain in a manner analogous to that in mammals. Thus, emphasis needs to be placed on the development of alternatives that replace, as much as possible, the use of all living vertebrate animals, including fish. This review gives the first comprehensive and critical overview of the existing alternatives for live fish experimental studies. The alternative methods described range from cell and tissue cultures, organ and perfusion models, and embryonic models, to in silico computer and mathematical models. This article aspires to guide scientists in the adoption of the correct alternative methods in their research, and, whenever possible, to reduce the use of live fish.