Squatiniformes was named by Buen (1926). It is extant.

It was reranked as the suborder Squatiniformes by Cassier (1966); it was reranked as the unranked clade Squatiniformes by Cicimurri et al. (2022).

It was assigned to Euselachii by Cassier (1966); to Squatinomorphii by Long (1992); to Squalomorphii by Biddle (1993); to Elasmobranchii by Peng et al. (2001); to Chondrichthyes by Purdy et al. (2001), Sepkoski (2002); to Neoselachii by Underwood (2006), Cicimurri and Knight (2009); to Squalimorphi by Long (2011); to Squatinida by Nelson et al. (2016); to Selachimorpha by Kent (2018); and to Squatinida by Cicimurri et al. (2022).