German Fallschirmjägers gained an almost mythical standing in the first couple years of WWII.
Sky soldiers of the 7th Flieger-Division cut off the evacuation of Polish officers in the invasion of that country in September 1939.
They made the the first airborne invasion when invading Denmark on the 9 April 1940, taking control of Aalborg Airport and other key strategic locations well behind the front lines by complete surprise. A sequel to this came the near simultaneous Norwegian campaign where German paratroopers captured the defended air base of Sola and leapfrogged around tough defensive obstacles to capture the rail junction at Dombas five days later (but was later taken prisoner by the Norwegians when they ran out of ammo– an important lesson that few airborne pundits kept in mind).
Then came Operation Fall Gelb during which Kurt Student’s Fallschirmjägers fell in little groups all over Belgium and the Netherlands capturing the bridges at Veldwezelt and Vroenhoeven along with the huge fort at Eben Emael. While most of these came out OK, (although Student caught a round from a Dutch infantryman’s Hemburg rifle), a larger effort to capture The Hague and the bridges around Rotterdam failed miserably as the paras went “a bridge to far” so to speak.
Nevertheless, Student’s paratroops were expanded into the 14,000-strong XI. Fliegerkorps, and, used in conjunction with follow-on airlifted troops, conducted the first mainly airborne invasion in military history in Operation Mercury when they dropped into Crete on May 20. While they won the 13-day battle, they faced a some 40,000~ Greek and Commonwealth troops who were ready for them– definitely not the ideal for a mass airborne jump.
On the first day, Student landed 750 glider troops and 7,200 paratroops– of which 80 percent wound up as casualties.
Here is a great older documentary about the battle that proved the end of large-scale German parachute operations just months after they were heralded as a strategic wonder weapon.