Berets of the United States Army
U.S. Army Special Forces wear the green beret because of their link to the British Commandos of World War II. The first Ranger unit, commonly known as Darby's Rangers, was formed in Northern Ireland during the summer of 1942. On completion of training at the Commando Training Depot at Achnacarry Castle in Scotland, those Rangers had the right to wear the British Commando green beret, but it was not part of the regulation uniform at the time and was disallowed by the U.S. Army. 
The 10th Special Forces Group (Airborne) had many veterans of World War II and Korea in its ranks when it was formed in 1952. Members of the 10th SFG began to unofficially wear a variety of berets while training, some favoring the red or maroon airborne beret, the black beret, or the green commando beret. In 1953, a beret whose design was based on that of the Canadian Army pattern, and which was rifle-green in color, was chosen for wear by Special Forces units.
History of the United States Army Special Forces
Since Operation Inherent Resolve began, U.S. airstrikes have been supported by Green Beret adviser teams, helping stop the advances of ISIL. Green Berets from the 5th SFG deployed to Jordan in support of OIR, several news outlets reported they were at the Prince Faisal Air Base in Al-Jafr working for a CIA program to train moderate Syrian fighters. On November 4 2016, a small convoy of carrying Green Berets were returning to the base after a training exercise when a Jordanian guard, after waving the first vehicle through the entry control point at the base, then opened fire on the second vehicle killing 2 Green Berets, U.S. troops from the vehicle behind opened fire, another Green Beret was killed but a fourth, who was wounded, shot the Jordanian, severely wounding him. On January 8 2017, a Green Beret assigned to 2nd Battalion 5th SFG, was killed in a non-combat-related incident in Jordan.