Sarcopterygii was named by Romer (1955). It is extant.

It was reranked as the subclass Sarcopterygii by Miles (1977), Gardiner (1982), Ahlberg (1991), Young et al. (1992), Chang and Zhu (1993), Yu (1998), Schultze (2001), Davis et al. (2004), Young and Schultze (2005), Clement (2005), Clement (2006) and Johanson et al. (2007); it was reranked as the class Sarcopterygii by Long (2011); it was reranked as the superclass Sarcopterygii by Betancur-R et al. (2013).

It was assigned to Teleostomi by Miles (1977); to Osteichthyes by Romer (1955), Daly (1973), Thurmond and Jones (1981), Gardiner (1982), Ahlberg (1991), Young et al. (1992), Chang and Zhu (1993), Yu (1998), Dineley and Metcalf (1999), Schultze (2001), Meyer and Zardoya (2003), Davis et al. (2004), Young and Schultze (2005), Clement (2005), Irmis (2005), Clement (2006) and Johanson et al. (2007); and to Osteichthyes by Friedman and Daeschler (2006), Qiao and Zhu (2009), Lu and Zhu (2010), Clement and Long (2010), Long (2011), Clement (2012), Lu et al. (2012), Betancur-R et al. (2013), Qiao and Zhu (2015), Smithson et al. (2016), Mann et al. (2017) and Clack et al. (2019).