World War I's static warfare and the widespread, seemingly senseless carnage that that static warfare engendered, provoked a great deal of innovative military thinking in the interwar period. Doctrines for the effective use of massed armor and for strategic bombing were developed by members of Europe's armed forces, and these doctrines played a very important role in the course of fighting during World War II. Airborne infantry was another of these innovations. First demonstrated in Italy in 1927, airborne units eventually formed parts in the armies of all major combatants; and these airborne units were regarded by their armies and by the forces that fought them as elite. German paratroopers were an integral part of the invasion of Crete in 1941, and massed landings of American and British paratroopers played a part in every major Allied offensive in North Africa and Western Europe. Modern armies continue to contain airborne units, but because of the experience in World War II with massed landings, most have evolved their doctrine for their use. The German paratroopers on Crete suffered huge casualties, and Allied landings were plagued by an inability to get the troopers to the drop zone consistently and efficiently.
The two most famous airborne units in the United States Army during World War II (and after) were the 82nd and 101st Airborne Divisions. Elements of the 82nd Airborne fought in North Africa, Sicily, Italy, France, Belgium, and Germany. The 101st fought exclusively in the northern European campaign initiated by the landings at Normandy in 1944. We typically think of airborne units as being exclusively composed of parachute infantry, but both of these divisions also had glider infantry and parachute artillery units. Both divisions were (and are) elite and amassed an amazing combat record during the war. By far the most famous exploit was the 101st's defense of Bastogne during the Battle of the Bulge in December 1944. Bastogne was an important crossroads town in Belgium that stood in the way of the German advance on Antwerp; and the 101st was one of the only units available to reinforce the line when the Germans attacked. Eisenhower ordered them trucked to Bastogne, even though they didn't have sufficient winter clothing or ammunition and were understrength from their fighting in the Netherlands in September and October. They were quickly surrounded, but they managed to hold the town under a relentless German attack until George Patton's Third Army broke through to reinforce and resupply them on December 26. The 101st received a Presidential Unit Citation for their defense of Bastogne, the first time that an entire division had ever been so honored.
The most famous unit within the 101st Airborne Division was Company E of the 506th Parachute Infantry Regiment. Company E's fame is partially due to its fighting record during the war, which was excellent, but mostly because Stephen Ambrose wrote a book about it (Band of Brothers: E Company, 506th Regiment, 101st Airborne From Normandy to Hitler's Eagle's Nest). I wish that I could say that the book is good, but I can't. It's execrable. The writing style is turgid, there are numerous narratives errors, and it reads more like hagiography than an honest history of the unit and the men who served in it. Fortunately, they made a movie based on the book (or, rather, an HBO miniseries); and in this case, the movie is much, much better than the book. There are 10 episodes following Company E's progress from training at Camp Toccoa in Georgia to preparations for the Normandy landings in England to the Normandy campaign, Operation Market Garden, Bastogne, and the surrender of Germany. It has the same battlefield realism that Saving Private Ryan is noted for, but its storyline and characters strain the bounds of credulity much less than that movie did. It's moving, entertaining, and educational, probably the finest World War II motion picture that I have ever seen. And would you believe that Donnie Wahlberg can act? (He plays Carwood Lipton, Company E's First Sergeant during the Bastogne campaign, and does so very well.)