This paper reviews the present state of our knowledge concerning a little known family of physonect siphonophores, the Rhodaliidae. The members of this family are unusual in that they are short-stemmed, with the cormidia basically arranged into spirals around the spheroidal corm, and with the nectophores forming a corona around the base of a greatly enlarged pneumatophore. Unique to these animals is the possession of a dorsal aurophore, a structure that contains the considerably expanded pneumatochone, or gas-secreting area, of the pneumatophore. These and other unusual aspects of the morphology of the rhodaliids are described and compared with those in the more typical, long-stemmed physonect siphonophore. The history of the family Rhodaliidae is reviewed. The 37 specimens recorded in the literature, 15 of which belong to one species, originally were described under ten specific names. However, four of these names generally have been treated as synonyms of others, leaving six species within five genera. Whenever possible the extant material has been re-examined and, in addition, new specimens of five of the species have become available for study, as well as specimens of two new rhodaliid species. These studies, together with some additional information, have led to the suggestion that two of the original species, previously synonymized with another, should be resurrected as valid species, although a certain degree of intuitive reasoning is applied in one case, based mainly on differences in the geographical and bathymetric distributions of the relevant species. The systematics of the rhodaliid species is reviewed in detail and a key is provided for their identification. Recently, observations have been made on two rhodaliid species in situ, and these have conclusively proven that these animals are unique among the siphonophores in that their habitat is not planktonic, as previous authors asserted, but benthic. The observations indicate that the animals float above the substratum, tethered to it, like hot-air balloons, by their tentacles. The re-adoption of a benthic existence has led to many unique features being evolved in the rhodaliids, and some of these are discussed. The extraordinary size of the pneumatophore, especially in comparison with the planktonic physonects, appears to be a necessity since the gas that it contains is required to offset the excess density of the corm and enable near-neutral buoyancy to be attained. In order that the huge volumes of gas may be secreted, sometimes at pressures exceeding 300 atm (3 x 10<latex>$^7$</latex> Pa) the gas gland or pneumadenia has become greatly enlarged and forms part of the peculiar structure, the aurophore. The role of both the pneumatophore and aurophore in buoyancy control is discussed in detail. One other outstanding feature of the rhodaliid siphonophores is the possession of two types of gastrozooid on its cormidial units. Only one of these gastrozooids carries a tentilla-bearing tentacle. The arrangement is thought to be a result of the necessity to adopt a method of feeding different from the more usual fishing net set by the planktonic siphonophores. There is little doubt, therefore, that the rhodaliids are a fascinating and very unusual family of siphonophores.