This phylograms is based directly on Smith, Pryer, Schuettpelz, Korall, Schneider, Wolf (2006). "A classification for extant ferns" ^[1]

This is based on Christenhusz et al.: A linear sequence of extant families and genera of lycophytes and ferns (2011)^[2] and Rai and Graham: Monilophyte Phylogeny (2010)^[3] Note that Equisetaceae branches first, and the Lindsaeaoid families are different than in the previous phylogram.

Same list, attempting to include classes and orders:

The following phylogram shows a likely relationship between the other vascular plant classes and the leptosporangiate ferns.^[4] Note that these relationships are far from settled. For example, this diagram shows Equisetopsida as a sister to Polypodiopsida. Depending on how the data was interpreted (e.g. using Parsimony vs. maximum-likelihood analyses), Equisetopsida could just as well have been placed a sister to a Marattiopsida/Polypodiopsida clade.^[4]

While it is generally accepted that the leptosporangiate ferns are monophyletic, it is considered to be likely that the eusporangiate ferns, as a group, are polyphyletic. As shown in the examples from three recently published phylograms in the following table, it can be seen that the four eusporangiate fern families do not form a single clade.