The comparative osteology and phylogenetic relationships of fossil and living paddlefishes (Polyodontidae) are investigated in detail for the first time. This peculiar, poorly known group is of great significance to phylogenetic studies of primitive actinopterygians, because it is one of only two chondrostean families that have survived to the present. Consequently the group is frequently used as an outgroup for studies of the many fossil chondrostean groups and for higher-level studies of actinopterygian (and even osteichthyan) interrelationships.The family has a long but spotty fossil record dating back to the Upper Cretaceous, including species represented by relatively complete skeletons or at least skulls. These relatively complete fossils are extremely rare and belong to the species †Paleopsephurus wilsoni MacAlpin, 1947 from the Upper Cretaceous Hell Creek Formation of Montana (redescribed here); †Polyodon sp. nov. from the lower Paleocene Tullock Formation of Montana (described here); and †Crossopholis magnicaudatus Cope, 1883 from lower Eocene deposits of the Green River Formation in Wyoming (described in detail here for the first time based on much new material). Among the fossils, †Crossopholis is of particular interest, because it is now known by several nearly complete skeletons (reported and described here for the first time). †Paleopsephurus and †Polyodon sp. nov. are known from a single partial skull each, and some fragmentary postcranial material, but are well enough represented to include in our phylogenetic analysis. Other, more fragmentary, Upper Cretaceous and Paleocene material (some newly reported here) is placed in Polyodontidae incertae sedis.There are two extant species in the family, frequently referred to in the literature as “living fossils.” These two species are Polyodon spathula from the Mississippi River drainage of North America, and Psephurus gladius primarily from the upper Yangtze River drainage in China. The osteology of Psephurus gladius is described here in detail for the first time.Previous studies of Polyodontidae have been almost exclusively based on Polyodon spathula, because specimens of the other species are extremely rare and very poorly known. After accumulating and preparing material for several years, we were able to describe more fully all polyodontid species and examine the family phylogenetically. Our study reveals that Polyodon spathula is a highly derived member of the family, and generally not a good representative of the family when the family is used as an outgroup for higher-level phylogenetic studies of actinopterygians. The use of Polyodon spathula as the primitive polyodontid has previously led to several serious errors in the literature. We therefore also summarize certain primitive characters of Polyodontidae in this paper.Contrary to previous studies, we show that †Paleopsephurus has the stellate rostral bones unique to polyodontids (in addition to the long median rostral bones and extremely elongate snout also unique to the group). Also contrary to previous studies, Polyodontidae (at least primitively) does have ossifications of the quadratojugal, interclavicle and postcleithrum. We also report several other osteological features previously unknown from the family.Our study results in a phylogenetic hypothesis for paddlefishes that is radically different from the only other published cladogram (Gardiner, 1984b). We demonstrate that †Paleopsephurus clearly belongs in Polyodontidae, rather than Acipenseridae as proposed by Gardiner (1984b). †Paleopsephurus is the sistergroup to Polyodontinae, new subfamily (a group containing Psephurus, †Crossopholis, and two species of Polyodon). Psephurus is the sistergroup to Polyodontini, new tribe (a group containing †Crossopholis and Polyodon). Polyodon contains the extant Polyodon spathula as well as a new fossil species from early Paleocene freshwater deposits of Montana.A better understanding of polyodontid osteology also enables us to provide a phylogenetic hypothesis for Acipenseriformes (assuming monophyly of Acipenseridae) that differs from that of previous authors. In particular we find that †Chondrosteidae is the sistergroup to a group containing Acipenseridae plus Polyodontidae. Polyodontidae also provide evidence that the supraneurals in actinopterygians are the serial homologues of epurals, and not of fin radials.As has previously been apparent, Polyodontidae is one of several groups that indicate a transpacific biogeographic relationship for western North America (west of the continental divide) during the Early Tertiary.We also describe ontogenetic and intraspecific variation in paddlefish osteology. Based on the large amount of variation, we conclude that, in at least some fishes, it is important to examine large numbers of specimens, including extremely old individuals (i.e., “upper end ontogeny”) in the developmental series to more completely document the morphology. Normal-sized, reproductively active adult paddlefishes lack particular ossifications of the scapulocoracoid, vertebral column and neurocranium present in other osteichthyans; but as we show here, these elements eventually ossify in very large, older individuals. In this sense, paddlefishes appear to be the axolotls of the fish world, offering one of the best documented cases of paedomorphosis (or neoteny) known to date.