Of all the world's militaries, the US military special forces community is the largest and the most technically oriented compared to other special forces in other militaries. As a side note, there is no such thing as 'Green Berets', only US Army Special Forces soldiers. These soldiers will tolerate 'Green Berets' at best and hate that label at worst.
Most people, even inside the US military structure either as civilian or military, are unaware that the US Air Force have its own special forces troopers. They are Combat Controllers, Pararescue, and Combat Weather. Despite the USAF's reputation for being a 'high tech' oriented service with the aircraft being the most visible symbol of the service, a long time ago, the USAF recognized the need to have its own special forces on the ground trained to exploit airpower to the maximum to increase the odds of victory for the other three branches that need air support, any time and any place.
A USAF Combat Controller is more than just an FAA certified air traffic controller. He is very much a combat soldier no less than a US Navy SEAL or a US Army Ranger. When earthquake ravaged Haiti needs air traffic controls despite the lack of a functioning airport tower, the USAF CCT team managed over two hundred aircrafts -- per day -- via their notepads and maps. Not counting basic arms, a CCT must be as certified in parachuting as a US Army Ranger, including high altitude free fall, and as at home in the water as a US Navy SEAL. If assigned with the US Army in directing artillery, he must be as proficient in trigonometry as any seasoned artillery US Army gun crew. In other words, he must know how to use any 3rd dimension weapon system to its maximum potential in combat.
Combat Weather are essentially 'killer' weathermen. Criticize their forecasts at one's peril. But more than that, each CW specialist must be educated in the natural sciences relevant to meteorology and oceanography, how local environment can affect and influence forces of friends and foes, and to fight when necessary. It take about 2 yrs of technical training in the hard sciences to qualify an apprentice Combat Weatherman. A CW could be deployed with an US Army Ranger unit, or a US Marine scout party, or a US Navy SEAL insertion team, and that mean his physical conditioning must be no less than those he support. In this age of warfare when air assets are often below cloud cover, such as the always critical helos, immediate meteorological intelligence and analyses, from the tropics to the poles, a CW is a vital asset to any special operations unit.
Of the three USAF special forces, a pararescueman, or pararescue jumper (PJ), is a bit of a contradiction. He is not a mere first aid specialist but a fully certified medic with the National Registry of Emergency Medical Technicians. He will be trained in minor field surgery that includes emergency airway clearance so his charge can breath, pharmacology, and even esoteric knowledge like collapsed structure reconnaissance and exfiltration. Downed pilots are/were not the only recipients of the PJs' skills but also victims of disasters, from natural to human caused. The contradiction lies in the fact that a PJ is not a medic under the Geneva Conventions despite his primary mission of being a life saver. Under the GCs, a medic must wear the distinctive red cross emblem somewhere on his person. A medic may carry a weapon, but he is not allowed to engage in combat. He will not display any distinctive emblems other than that of the US military. But a PJ is a specialist in covert insertion, tracking, survival, and recovery of friendly airmen behind enemy lines and will engage in combat and kill if necessary in his mission.