The concept of “mosasaur” is explored from the perspective of its historical origins, and tested empirically and phylogenetically in order to examine the concept in its modern application. Historical analysis of the origins of the concept of “mosasaur” makes it clear that the term bears significant historical burden (comparative anatomic, empirical, phylogenetic, paleontological, etc.). In order to address the flaws in the concept of mosasaur properly, this treatise critically assesses Camp’s  diagnostic characters for Anguimorpha, Platynota, Varanoidea, and Mosasauroidea, concluding that Camp’s data permit mosasaurs to be viewed only as anguimorphans, not platynotans nor varanoids. A similar critical assessment is given for the characters used to diagnose anguimorphans and varanoids in Estes et al. , concluding here that not a single character out of twenty-two is shared between varanoids and mosasaurs. The character concept developed by Romer  for the “posteriorly retracted nares” of varanoids, and then later mosasaurs, is critically examined and found to be insufficient as a test of similarity of the intended primary homologs. The recent work of Rieppel et al. , Conrad  and Conrad et al.  is critically reviewed as these authors revive the use, and subdivision, of the “posteriorly retracted nares” as a character in anguimorph phylogenetic analysis. Based on these criticisms, it is concluded here that there is no character-based evidence to support phylogenetic hypotheses that mosasaurs are derived aquatic varanoid lizards. A key recommendation of this treatise is that the hypothesis conceiving of mosasaurs as derived aquatic varanoids be abandoned. The final critical review presented in this treatise examines the taxonomic implications, relating to the concept of “mosasaur”, arising from the hypothesis of convergent paddle-like limb evolution in mosasaurs as presented by Bell and Polcyn . In conclusion, it is recognized that the concept and term “mosasaur” has ceased to exist in any biologically meaningful way, and that the future requires the construction of a new suite of terms and concepts to convey what we now think we know about these animals.