There are around 6000 species and they come in two morphological types.
They can form extensive mats on still water.
The leafy liverworts are much more common than thallose ones.

Leafy liverworts.

These have stems and leaves so resemble mosses but the leaves have no midribs.
Most are prostrate and grow on soil, leaf litter, bark or rocks.
The stems are flattened and the leaves can be in 2 ranks or more often 3 rows made up
    of 2 lateral rows and a smaller flattened row underneath.

Leaves are small, often about 1 mm long and only 1 cell thick.
Shape varies from round to much lobed and the margins may be toothed or hairy.
Some are folded to form pockets.
They may overlap each other.

Rhizoids grow from the undersurface of the stems or leaves.
They may be short, simple or branched.

The capsules, usually black and variously shaped, are typically on soft stalks which are short
    and transparent (mosses stiff and opaque, often dark).
Capsules release spores via slits and the segments may roll back.

Microscopy is often needed to differentiate between species and from mosses.

Thallose liverworts.
These are flat, usually green, prostrate plants that are undifferentiated into stems and leaves.
Most parts are small, 2 – 20 mms wide with individual plants less than 10 cm long.

They may or may not branch several times into equal sections.
They have rhizoids similar to mosses.
Spore capsules can be on stalks or embedded in the thallus.