The aim of the present paper is to give, as concisely as possible, the summary of two years' work on the caudal fins of fishes and also to revise the definitions relating to the different types of caudal fin. The revision of the definitions of old established names such as protocercy, heterocercy, etc., has proved to be quite essential owing to the vagueness and even errors connected with these terms so much in evidence in text-books of zoology; this vagueness undoubtedly exists, or otherwise such mistakes as attributing diphycercy to such types as the Gadidæ and the eels would not occur as they do. I have also been assured by several eminent teachers of zoology that the subject needs clearing up. The whole of my work has included the examination of well over a hundred different species of fishes representative of nearly all the sub-groups of Teleosts, several Ganoids, and a few Elasmobranchs. Probably the most interesting results have been obtained from the Gadidæ and Apodes and the frequent misinterpretations to be read on the caudal fin of these groups has convinced me that caudal fins have not been subjected to a sufficiently close structural examination; for this reason I have made a point of examining microscopically every tail fin, and have invariably subjected each one to clearing agents, a process which has revealed many features it is impossible to recognise by mere dissection.