Hoploparia McCoy, 1849 (Lower Cretaceous (Valanginian)–Miocene) is, by far, the most diverse clawed lobster genus (fossil or Recent); 49 species are known. The genus has been interpreted intuitively to be morphologically primitive and ancestral to some or many modern nephropid genera. Prior to the present study, two separate issues raised the suspicion that Hoploparia is a “wastebasket” genus—a default genus for any fossil lobster with a mainstream nephropid morphology. One issue is the difficulty in characterizing (i.e., coding) the morphology of Hoploparia, as a genus, for cladistic analysis. For Hoploparia, and far more than for other lobster genera, many characters show variable character states. A second issue is that the morphologies of some Recent genera (e.g., Eunephrops and Nephropides) seem easily accommodated within the fossil genus Hoploparia. Both issues stem from an originally ambiguous diagnosis of Hoploparia that has been variously expanded in de facto fashion to the point that, today, nobody really knows what Hoploparia means. Cladistic analyses herein indicate that Hoploparia is paraphyletic and, therefore, support the intuitive judgement that Hoploparia is a wastebasket genus. This paper, the first species-level cladistic analysis of Hoploparia, is not intended to be the sole basis for taxonomic revision but is, instead, intended to generate discussion among lobster specialists. Hopefully, this discussion will bring forth additional characters for cladistic analysis and other new insights that may lead to better supported cladograms addressing lobster taxonomy.