One of the Olympic forms of wrestling, the Greco-Roman rule set, is one of the widest spread forms of wrestling in the world. Greco-Roman wrestling produced some of MMA's biggest stars. Its oddly specific rule set has benefited many of its fighters.
Brief History: The history of this art is often misunderstood because the name suggests origins in Ancient Greece and Rome. But that is not the case, the wrestling of that age was actually more similar to Freestyle wrestling than the style which wears the name Greco-Roman. Greco-Roman originated with a French solider in Napoleon's army named Jean Exbrayat. It is thought that Greco-Roman Wrestling is a combination of several local European wrestling styles, and in Napoleon's army Exbrayat would have been ideally placed to collect grappling knowledge as Napoleon marched his troops all over Europe.
In 1848, Exbrayat established rules outlawing submission holds and any grips below the waist. Known as "Flat Hand Wrestling" or "French Wrestling" at the time, it spread through Europe and became very popular. Italian wrestler Basilio Bartoli is the one who coined the phrase "Greco-Roman Wrestling" in an attempt to connect the wrestling to ancient values and competition. It became so popular that it was included in the first modern Olympics in 1896, and has been in every Olympic Games since save the 1900 Paris Games.
Summary of Rules: The single biggest difference between Greco-Roman and other forms of wrestling is that no grabs below the waist are allowed, meaning the that grappling is exclusively upper-body. Pins end a match, and in absence of a pin the match is determined by points. Those points are awarded for throws - the more spectacular and clean the throw the more points it is worth - escapes, back exposure, and forcing an opponent out of bounds.
There are a huge number of rules in Greco-Roman wrestling that strictly dictate the athlete's actions, everything from head placement in the clinch, gripping, body position, to lower body contact is regulated in some form. It is a difficult and very complex rule set in which to compete.
Strengths: Greco-Roman wrestlers are very strong in the clinch. The upright, clinch grappling that takes place in a Greco-Roman match transfers very well to MMA clinch fighting. Unlike Judo, which also excels in the clinch, the jacket-less grappling of Greco-Roman jumps over to MMA with a shorter learning curve. The battle for underhooks and the proper use of overhooks is central to success in Greco-Roman wrestling.
And in that clinch, the Greco-Roman wrestler has a good number of takedowns, throws, and suplexes. (Gif) (Gif) (Gif) Also, with the restrictive rules removed, Greco-Roman wrestlers are free to incorporate takedowns that would otherwise be illegal (Gif) or modify Greco-Roman style takedowns with illegal details, like a knee-on-knee block. (Gif)
When speaking of Greco-Roman wrestling and MMA, it is important to mention that one of the first grounds of American wrestlers to experienced sustained success were the Greco-Roman based fighters at Team Quest, most notably Matt Lindland, Randy Couture, and Dan Henderson. Together they pioneered modern MMA skills such as cage wrestling, the ability to use the cage both to prevent and aid with takedowns. They also developed "dirty boxing" which involved punching into the clinch, striking while in the clinch, and to land punches while exiting the clinch.
On the ground, Greco-Roman wrestlers are adept at controlling and pinning their opponents. Greco-Roman fighters are well known for their physical strength, both with grips and with squeezing in the clinch. Also, many wrestlers transition to Greco-Roman wrestling from Freestyle, so they are accustomed to adjusting how they grapple and approach competition to fit a strange ruleset.
Weaknesses: The biggest weakness is the lack of lower body attacks. Greco-Roman are vulnerable to lower body attacks like trips, and can be taken down by less accomplished grapplers. (Gif) (Gif) (Gif) This deficiency is a serious impediment, and it is no accident that the most accomplished Greco-Roman wrestlers in MMA also competed in American Folk Style as well.
On the ground, Greco-Roman wrestlers are experienced grapplers, but they aren't exposed to aspects of positional grappling, like guard passing or back control, or submission grappling.
So, while Greco-Roman wrestling does provide a strong grounding in certain aspects of the required skillset for MMA, it requires a good deal of additional skills to be made into a strong MMA base. But when those additions are added, the base in Greco-Roman wrestling can result in a very successful fighter.
Video of Grappling Art: