In the late 1830's Charles Darwin spent several years in South America studying crustal movements, elevation, and subsidence. Along with Charles Lyell, he sought an answer to the question of South America's elevation. Ironically, his work on subsidence led to a now universally accepted theory of reef formation.  In his 1842 report Coral Reefs, Darwin grouped coral reefs into three distinct types: barrier, fringing, and atolls. He then explained that each reef type was really a separate stage of reef development around a slowly sinking volcanic island. 
Stage 1 - Fringing Reef A submarine volcano forms an island rising from the sea floor. Corals begin to grow in the shallow regions off the coast of the island. As the island gradually sinks, the reef grows upward in order to stay within a sunlit range. A fringing reef is a reef encircling this volcanic island while it first begins to sink.
The Deep Sea Drilling Project sought evidence of volcanic cores beneath coral reefs and found it. First, in 1952 at the Einwetok Atoll in the Marshall islands, and again, in 1960 at the Midway Atoll, teams found volcanic rock strongly supporting Darwin's theory that coral reefs form around submerging islands. Today, Darwin's theory is universally accepted as a means of explaining these reef formations. 
While many of the Pacific reefs form around islands as Darwin's theory describes, this is not the case in the Caribbean where there are few atolls. Here, other reef types like patch and bank are also exhibited and form separately than Darwin's theory describes. 
- Burkhardt, Frederick. "Darwin and Coral Reefs." Darwin Correspondence Project. University of Cambridge, 2012. http://www.darwinproject.ac.uk/darwin-coral-reefs 25 Feb 2013.
- Strykowski, Joe and Rena M. Bonem. Palaces Under the Sea. Crystal River, FL: Star Thrower Foundation, 1993, p. 19-26. Print.
- Strykowski and Bonem, p. 19
- Alevizon, William. "Types of Coral Reefs." http://coral-reef-info.com 2012. Web. 25 Feb 2013.