"In 1957, a small group of ex-service pilots pooled their money to purchase a P-51 Mustang, beginning what is now called the Commemorative Air Force (CAF). With the addition of a pair of F8F Bearcats, the CAF became the founders of the Warbird Movement, an effort to preserve and honor our military aviation history with the rallying cry “Keep ‘Em Flying!” Now, nearly 60 years later, the CAF operates 164 flyable vintage aircraft for the education and enjoyment of present and future generations." ---CAF brochure
The rest of the story...
Ralph Royce and Lefty Gardner used to do "demonstrations" at early "air shows" and county fairs in Texas. Ralph had the P-51 and Lefty had a P-38 which, later, many folks knew as "White Lightning". Many times the airstrips that the demonstration aircraft would operate from in those days weren't always "improved" a whole lot from a few dozer passes through what was previously a field. Following one of the demonstrations, the pilots had parked their airplanes beside the dirt runway and had retired to the "BBQ" portion of the "air show". While walking around the "used WWII airplanes" that Lefty and Ralph were flying, one of the attendees took his finger and, in rather large letters, wrote "Confederate Air Force" in the dust on one of the tail booms of the P-38. Good ol' boys that they were, Ralph and Lefty used that appellation at air shows for years.
In more recent times, it is still the CAF, however the "politically correct" appellation currently is the "Commemorative Air Force". It is the only "flying museum" of WWII aircraft in the world, really.* The collection, which is extensive, FLYS. There are "wings" of the CAF all over the country, and it's lifeblood are well-qualified volunteers. It is a great organization for folks who have either skills, or true interest, in WWII airplanes to look into.
*It must be noted that there are, certainly, a couple of Foundations and private collections which have multiple aircraft. However, none of them are more extensive than the Commemorative Air Force's collection. At one time, the "Confederate Air Force" was the 6th largest Air Force in the world.