The two most important new concepts in warfare in this war were blitzkrieg and strategic bombing.
The concept of blitzkrieg was of war based on rapid mobility and close coordination between various parts of the armed forces (armor, infantry, air support, artillery). This doctrine was used to great effect by the Germans early in the war and was emulated by the Allies later on.
Strategic bombing was the idea of using masses of bombers to hit industrial and transportation targets as opposed to military targets. The idea had been around since WWI, but the technology had not yet enabled air forces to do this until WWII. Strategic bombing was critical to the Allied defeat of the Axis.
One other new concept, which might rightly be considered part of the 'blitzkrieg' doctrine, was the use of airborne forces, both paratroopers and glider-borne.
These concepts were first pioneered by the Soviets, and then developed and put into practical use by the Germans. They reached their zenith when the Allies launched the ambitious Operation Market-Garden (made famous by the book A Bridge Too Far).
Some Airborne Operations of Note:
Glider-borne Assault on fortress of Eban-Emael (May 1940)
Operation Merkur - Airborne Assault on Crete (May 1941)
Glider-borne Rescue of Mussolini (September 1943)
Parachute Drop at the Battle of the Bulge (December 1944)
Airborne Assault on Sicily, part of Operation Husky (July 1943)
Airborne Assault for the Invasion of Normandy (June 1944) in particular: Glider-borne Assault on Pegasus Bridge
Operation Market Garden (September 1944)
As Operation Merkur was the most ambitious German Airborne operation, so too Operation Market Garden was the most ambitious Allied Airborne operation, and in fact employed more paratroopers than had Merkur.
Although the paratroopers in both operations fought with skill and determination, the results in each assault were less than satisfactory. For the Germans, the heavy casualties on Crete convinced Hitler that the day of the paratrooper had passed and with the exception of limited small operations, the German paratroopers were relegated to the role of elite ground infantry.
Likewise, after the heavy losses suffered during Market-Garden, the Allied Airborne Forces spent the remainder of the war in a elite ground combat role. Plans were drawn up for several airborne assaults, but again, except for small limited operations, there were no major assaults or parachute drops. This was due, in large part, to the rapid collapse of Germany after the Battle of the Bulge and the lack suitable targets for an airborne assault.
A small side note: In 1962, Operation Deadstick featured in Darryl Zanuck's film The Longest Day which was based on the book of the same title by Cornelius Ryan. Major John Howard was played by Richard Todd who had been an officer in the 7th Parachute Battalion during the battle.