Undulatory swimming in fish is powered by the segmental body musculature of the myotomes. Power generated by this muscle and the interactions between the fish and the water generate a backward-travelling wave of lateral displacement of the body and caudal fin. The body and tail push against the water, generating forward thrust. The muscle activation and strain patterns that underlie body bending and thrust generation have been described for a number of species and show considerable variation. This suggests that muscle function may also vary among species. This variation must be due in large part to the complex interactions between muscle mechanical properties, fish body form, swimming mode, swimming speed and phylogenetic relationships. Recent work in several laboratories has been directed at studying patterns of muscle power output in vitro under simulated swimming conditions. This work suggests that the way that fish generate muscle power and convert it into thrust through the body and caudal fin does indeed vary. However, despite the differences, several features appear to be common to virtually all species studied and suggest where future effort should be directed if muscle function in swimming fish is to be better understood.