Corals are in the phylum CNIDARIA. Corals belong to the class ANTHOZOA and hard corals are divided into 3 orders: Tabulata , Rugosa and Scleractinia. There are other groups within the Anthoza, including soft corals.

The Rugosa or "rugose" corals are known for their wrinkled appearance which is where they get their name. The best known Rugose corals are the solitary "horn" corals which can be found in nearly every fossil collection. These are shaped like simple horns and bear a superficial resemblance to snail shells. This is a good example of animals that are quite different coming up with a similar solution to meet a similar need.

Rugose corals had colonial as well as soliary forms and were nearly as diverse in their day as modern corals are now. Many striking examples of colonial rugose corals can be found in fossil collections though they aren't nearly as common as the tabulate corals, which dominated the paleozoic era, and, together with bryozoans, were the primary reef builders.

The Tabulata or "tabulate" corals were as dominant a feature in their time as modern corals are today. Their most striking feature, which also gives them their name, is the horizontal shelves or "tables" that seperate old living compartments from newer ones. These are best seen in cross section and give a good estimate of how many generations of polyps formed the coral colony.

The modern hard corals, Scleractinia are not generally believed to be an offshoot of either tabulate or rugose corals but are thought to have developed from a more primitive, perhaps solitary, group which diversified to fill the ecological gap left behind by the rugose and tabulate corals after the permian extinction.

The hard skeletal structure which is formed by secretions from the coral polyps is often found in the fossil record but the polyps themselves, lacking hard parts, are not usually preserved. This is causes problems in recognizing fossils because animals that were quite different often left similar looking skeletons. Bryozoans, for example, left structures that look a lot like coral skeletons and the shells of ammonites look a lot like snail shells although the animals themselves, while being mollusks, were not gastropods and were much more like octopuses than like snails!

There are many resources both on the web and elsewhere which contain additional information about both the fossil and modern forms of this fascinating group.