This paper deals primarily with (and describes) the family Amphiuridae in Mortensen's sense, that is excluding Ophiactis and its allies, although it was necessary to include Aphiactis, mainly because of a nomenclaturial problem. The relationship between the Amphiuridae and the Amphilepididae is reviewed with the result that the Amphilepididae is reduced to the rank of a subfamily. The taxonomic weight of various characters which have been used in grouping the species of amphiurids is assessed and a modified formula for expressing oral armament concisely is introduced. The family Amphiuridae now consists of over four hundred nominal species of ophiuroids, most of them living on or burrowing in more or less muddy sand or gravel and some of them very delicate, easily losing the disc, so that a few species are known only from incomplete specimens. The family has recently (1962) been the subject of a revision by Fell, who has divided the larger genera Amphiura, Amphiodia, Amphipholis and Amphioplus into groups of more manageable size which are unfortunately rather artificial in my opinion. Hence, a summary of proposed taxonomic changes and a list of transfers of species to different genera (or families) are included at the end.