After Parker, 1982, De Luna, Newton & Mishler, 2003a, b ["The Tree of Life"], and Steward & Rothwell, 1993

<==o Bryophyta (peristomate mosses; lehtisammaleet)
   |--o Sphagnopsida (peat mosses, sphagnums; rahkasammalmaiset kasvit)
   |  |?- †Protosphagnum [Protosphagnales]
   |  `--o Sphagnales
   |     `--o Sphagnaceae (peat mosses, sphagnums; rahkasammalet)
   |        `-- Sphagnum
   |--o Andreaenopsida (lantern mosses)
   |  `--o Andreaeales
   |     |-- Andreaeaceae
   |     `-- Andreaeobryaceae
   `--o Bryopsida (peristomate mosses; lehtisammaleet)
      |?- †Musites polytrichaceus
      |?- Oedipodiaceae
      |--o Polytrichideae [Polytrichopsida sensu De Luna, Newton & Mishler, 2003] (hair-cap mosses)
      |  `--o Calomniaceae
      |     `-- Polytrichum
      `--+--o Tetraphidadeae [Tetraphidopsida sensu De Luna, Newton & Mishler, 2003]
         |  `-- Tetraphidaceae
         `--o Bryideae [Bryopsida sensu De Luna, Newton & Mishler, 2003] (aitosammaleet)
            |-- Diphysiales
            `--+?-o Funariales
               |  |-- Funariaceae
               |  |-- Pseudoditrichaceae
               |  |-- Disceliaceae
               |  |-- Gigaspermaceae
               |  `-- Ephemeraceae
               `--+?-o Timmiales
                  |  |== other Timmiales??
                  |  `-- Timmiaceae
                  `--+?-o Encalyptales
                     |  `-- Encalyptaceae
                     |-- Dicraniidae (dicraniid mosses)
                     `-- Bryidae (bryid mosses)

Mosses not listed by De Luna, Newton & Mishler, 2003b

    Takakiales
        Takakiaceae [sometimes ttreated as Hepaticopsida]

    Isobryales
        Fontinaliaceae
        Hydropogonaceae
        Wardiaceae
        Climaciaceae
        Leskeaceae
        Fabroniaceae
        Cryphaeaceae
        Leucodontaceae
        Regmatodontaceae
        Hedwigiaceae
        Cyrtopodaceae
        Prionodontaceae
        Lepyrodontaceae
        Rutenbergiaceae
        Trachypodaceae
        Pterobryaceae
        Meteoriaceae
        Ptychomniaceae
        Neckeraceae
        Phyllogoniaceae

    Buxbaumiales
        Buxbaumiaceae

    Fissidentales
        Fissidentaceae

Reference(s):