Wrestling was a focus of the first modern Games in Athens 1896. Greco-Roman wrestling was deemed a pure reincarnation of ancient Greek and Roman wrestling. Eight years later at the St. Louis 1904 Games, Olympic officials added the freestyle wrestling category because of its popularity. Commonly known as “catch as catch can”, freestyle wrestling had become the staple form of professional entertainment in 19th-century fairs and festivals in Great Britain and the United States. And, it became a staple of the Games themselves. The women category was introduced in freestyle wrestling at Athens 2004.
Competition:
Wrestling is a grappling sport - the aim is to force your opponent to the ground. Matches take place on a mat, and last for three periods of two minutes, with a 30-second break in between.
There are two styles of Wrestling at the Games: Greco-Roman and Freestyle. In Freestyle, competitors can use all parts of their body to do moves and holds. In Greco-Roman, use of the legs to make contact is forbidden.
A wrestler wins the match when he has won two out of three periods. For example, if one competitor were to win the first period 1-0 and the second period 1-0, the match would be over. However, if the other competitor were to win the second period, then a third and deciding period would result. Only a fall, injury default, or disqualification terminates the match; all other modes of victory result only in period termination.
So it is possible for the losing wrestler to outscore the winner. For example, periods may be scored 2-1, 0-3, 1-0, leading to a total score of 3-4 but a win for the wrestler scoring fewer points.
List of Events:
Wrestling Freestyle
Jargon Buster:
Related Websites:
International Federation of Associated Wrestling Styles (FILA Wrestling)
Wikipedia: Wrestling at the Summer Olympics

Thanks for the wonderful intro!