Ascophora was named by Levinsen (1909). It is extant.

It was corrected as Ascophorina by Gordon et al. (1994), Gordon and Taylor (1999), Guha and Gipikrishna (2007); it was reranked as the infraorder Ascophora by Grischenko and Gordon (2004), Di Martino and Taylor (2013); it was synonymized subjectively with Flustrina by Gordon (2012); it was reranked as the infraorder Ascophorina by Berning (2006), Di Martino and Taylor (2015).

It was assigned to Cheilostomatida by Gordon et al. (1994), Pouyet (2000); to Neocheilostomina by Grischenko and Gordon (2004), Berning (2006), Guha and Gipikrishna (2007); and to Cheilostomata by Canu and Bassler (1935), Brown (1952), Bassler (1953), Brown (1956), Brown (1958), Cheetham (1962), Scolaro (1970), Cheetham (1972), Boardman and Cheetham (1987), Gordon and Taylor (1999), Schmidt (2003), Zagorsek et al. (2010), Zagorsek and Gordon (2013), Di Martino and Taylor (2013), Di Martino and Taylor (2015).