Hepatopsida / Hepaticopsida: The Liverworts consist of 46 families with around 7.000-8.500 members of which 150 can be found in Denmark, called "Levermosser". Liverwort leaves are arranged in one plane, the capsules and seta are brown, and opens as an umbrella.

Anthocerotopsida: The Hornworts is a smaller group with only three families and 300 members of which only two can be found in Denmark: "Ru Hornkapsl"; Anthoceros punctatus ssp agrestis and "Glat Hornkapsl"; Phaeoceros leavis spp carolinianus. The characteristic is that the sporophyte continues to grow throughout its life, forming the "horn".

Sphagnopsida: The Peat Moss class contains of only one family with around 200 species. 40 can be found in Denmark, known as "Tørvemosser" or "Spagnummosser". It has a peculiar structure where its branches produced in fascicles or two or more diverging branches and two or more pendant (hanging) branches. Their spores sits close around the top of the plant.

Andreaeopsida: The Granite or Lantern Mosses are divided into two families; Andreaeaceae and Andreaeobryaceae which only hold around 60-100 species, 40 found in Denmark, known as "Sortmos". Their distinctive features are; the protonemata (the earliest stage in growth of a moss from the spore) have a different structure from other mosses; they are thallose, forming a multicellular flattened layer of embryonic cells. Further more, the lantern mosses also release their spores differently. Where the Bryopsida have a stalked capsule whose top falls off to release the spores, the capsules of lantern mosses have no stalk, no cap, and no teeth. Instead, the capsule is elevated on an extension of the plant to which it is attached.

While living in South Africa, I had  other mosses. Even more South African mosses.
And some Danish mosses.