[4] As of 2021[update], WoRMS recognizes the following two species:[4] The genus was circumscribed by William A. Newman in 1982.

His original list of subgenera and species for the genus was the following:[3] Newman noted there were multiple fossil taxa in this genus, but didn't classify any except for the type species †C.

He created a new subfamily, Concavinae, with Tamiosoma Conrad, 1856 (the senior synonym of Menesiniella according to Zullo[b]), Arossia and Concavus among its genera.

[1] This genus is known in the fossil records from the Oligocene to the Quaternary (age range: from 28.4 to 0.012 million years ago).

Fossils are found in the marine strata of United States, Italy, Mexico, Morocco, Algeria, France, Haiti, Madagascar, Panama, Colombia and Slovenia.