The leptosporangiate ferns were first recognized as a group, the "Leptosporangiateen", by
Karl Ritter von Goebel in 1881, who placed the eusporangiate ferns with seed plants and vascular plants into a coeval "Eusporangiateen". As this classification artificially split the ferns,
Christian Luerssen subdivided the
homosporous ferns only into Eusporangiatae and Leptosporangiatae in 1884–9. The latter group was treated at a variety of ranks in subsequent systems of classification. The subclass "Polypodiidae" was first published and used for the homosporous leptosporangiate ferns by Cronquist, Takhtajan and Zimmermann in 1966, typified on
Polypodium L.. Other contemporary classifications used the name "Filicidae" for this subclass. Smith et al. (2006) carried out the first higher-level classification of ferns based on
molecular phylogenetics. They included
heterosporous water ferns (
Salviniales) (placed in a separate subclass by Cronquist et al. due to their highly modified morphology) within the leptosporangiate ferns, which they elevated to the rank of class as the
Polypodiopsida (published by Cronquist et al. to include all ferns). The common ancestor of Salviniales, Cyatheales and Polypodiales went through a
whole genome duplication. Later classifications renamed the group Polypodiidae, initially as a subclass of
Equisetopsida sensu lato. This subclass comprises leptosporangiate ferns as opposed to the remaining three subclasses which are informally referred to as
eusporangiate ferns. The following diagram shows a likely phylogenic relationship between subclass Polypodiidae and the other Equisetopsida subclasses in that system In 2014, Christenhusz and
Chase grouped all the fern subclasses together as Polypodiophyta and in 2016 the Pteridophyte Phylogeny Group (PPG) adopted the class Polypodiopsida
sensu lato for the four fern subclasses. The following
cladogram shows the phylogenic relationship between the subclasses according to the PPG. The first three small subclasses being informally grouped as
eusporangiate ferns, in contrast to the Polypodiidae or leptosporangiate ferns. Polypodiidae is shown as a
sister group of Marattiidae. }}
Subdivision In both the Christenhusz and Chase, and the PPG classification, the extant Polypodiidae are divided into seven orders, 44 families, 300 genera, and an estimated 10,323 species.
Phylogenetic relationships The following phylogram shows a likely relationship between the other vascular plant classes and the leptosporangiate ferns. It was formerly unclear about the relationship between
Equisetopsida,
Psilotopsida, and
Marattiopsida, but recent studies have shown that Equisetopsida is most likely sister to Psilotopsida. ==Discussion of molecular classification==