Asplenium is a genus of around 700 species in the family Aspleniaceae and is considered by most botanists the only genus of the family. There is great variety within the genus and species are grouped into several categories that are sometimes considered separate genera.
Cystopteris is a genus of 18 similar species in the family Athyriaceae with a global distribution. One species is native to Iceland and common in all regions of the country.
Dryopteris is a genus of around 150 species in the family Dryopteridaceae with a global distribution, although most species grow in temperate regions of the northern hemisphere. Two species are native to Iceland.