Plants -- includes all the familiar plants, and the unfamiliar, ranging back to primitive algae. They have chlorophyll in their cells and photosynthesize. Plants are very common as fossils, mainly as impressions with a carbon residue. Coal beds represent ancient swamps where plant life was so prolific, that it accumulated, one log and twig and leaf upon the other, to later become compacted into dense carbon-rich coal seams and layers within sedimentary rock.
Of course, plants form a hugely diverse group. We can focus on several particular fossils from the "Coal Age" (the Pennsylvanian, or the broader time unit, the Carboniferous ) as examples of how plants fossilize, and how we may have living representatives of ancient fossil lineages.
These are fossils of Calamites , a plant that grew to be tree size, even though it was a plant reproducing by spores, which we compare to day to ferns, a group that doesn't include many large forms. Calamites specimens show the familiar jointed pattern along the stem, even in small fragmentary pieces:
You see the pattern of the plant, but it has been flattened by the compression of burial, typical for plants, and it happens even in large dinosaur bones. A tyrannosaur skull could have been more than a meter wide in the living animal, but after burial, it can be compressed down by two-thirds. Imagine what happens during burial to plants, which over time will compress even more than dense bone.
The story for Calamites , and the group that includes it, is an interesting one. Calamites and related forms went extinct at the end of the Paleozoic Era, but an offshoot -- a close relative from the Coal Age -- lived on, and today we have a very similar plant called the horsetail, which can be seen growing along sandy stream banks (Rush Creek, southeastern Texas; Randall Terry, botanist, for scale):
If you look at the stem of horsetail plants ( Equisetum ), you see the familiar jointed pattern along the stem seen in Calamites :
Such examples are great for appreciating that the form of Life, whether plant, animal, protist, or bacterium, may hold a common pattern in a lineage for millions of years. Of course, we see at least some variation -- Equisetum plants are not very large, compared to their Paleozoic counterparts -- but we see evidence of genes remaining from the Coal Age.
Another fossil from the Coal Age is Lepidodendron , called that because of the scale-like pattern left when leaves fell off the plant as it grew larger (lepido = scale; dendron = tree, in this sense):
Image Source: Wikipedia
This is the pattern of the bark, which really does look like fish scales in some specimens , hence the funny name. The leaves of Lepidodendron and relatives were frond-like:
Make sure you look at the images on this Illinois Geological Survey web page , which includes views of great specimens of Lepidodendron and other plant fossils from the Coal Age. Here, two coal miners examine plant fossils on the roof of a coal seam, after the coal has been mined out of the seam:
Image Source: Illinois Geological Survey
Lepidodendron was a large tree, but belongs to a group that includes small plants today, the club mosses:
The plant (Rush Creek, southeastern Texas) with little branching leaf-like structures is Selaginella , a club moss, paling in comparison to the large trees, typical of this general plant group back in the Carboniferous.
We could go on and on showcasing plant fossils, but you have a taste. Paleobotany is the study of fossil plants, a fascinating course of study, with plenty of opportunity for new discoveries.