Fallschirmjäger were established in 1938. They had to train hard. If you was a NCOs, officer or other rank of the Luftwaffe you had to successfully complete six jumps in order to receive the Luftwaffe Parachutist's Badge. Nevertheless, during World War II, the Fallschirmjäger were seldom used as parachutists.

The Fallschirmjäger were famous for their willingness to give every effort unwaveringly even in the grimmest of situations. Instead, they were prized for their combat abilities and frequently acted in a "fire brigade" role as roving elite infantrymen. The Fallschirmjäger were very effective when used in commando style raids. 

Many units were part of this elite corps: 1st Parachute Division, formed in 1938; 2nd Parachute Division was formed in early 1943; 3rd and 4th Fallschirmjäger divisions formed in late 1943; 5th, 6th and 7th Fallschirmjäger divisions formed in 1944; and 8th, 9th and 10th Fallschirmjäger divisions formed rashly in 1945. The 20th and 21st Fallschirmjäger divisions formed in March 1945, never saw combat. Other independent regiments and brigades were: Ramcke Parachute Brigade formed in 1942, Luftlande-Sturm-Regiment formed in November 1939, Fallschirmjäger-Regiment Hübner formed in August 1944, 500th SS Parachute Battalion formed in October 1943 and 600th SS-Parachute Battalion formed in November 1944.  Also were parachute units: Brandenburger Regiment, 22nd Air Landing Division, and 91st Air Landing Division.

Kurt Student  was the German paratroop general in the Luftwaffe during World War II. Fallschirmjäger saw action in their proper role during 1940–1941, most notably in the capture of the Belgian army fortress at the Battle of Fort Eben-Emael and the Battle for The Hague in May 1940, and during the Battle of Crete in May 1941. However, more than 4,000 Fallschirmjäger were killed during the Crete operation. Afterwards, although continuing to be trained in parachute delivery, paratroopers were only used in a parachute role for smaller-scale operations, such as the rescue of Benito Mussolini in 1943. 

Fallschirmjäger formations were mainly used as crack foot infantry in all theatres of the war. During 1942 surplus Luftwaffe personnel (see above) was used to form the Luftwaffe Field Divisions, standard infantry divisions that were used chiefly as rear echelon units to free up front line troops. From 1943, the Luftwaffe also had an armoured paratroop division called Fallschirm-Panzer Division 1 Hermann Göring, which was expanded to a Panzerkorps in 1944.

Here I leave many recolored images from German Federal Archive (Deutsches Bundesarchiv) and two versions of the same original colour video on the Fallschirmjäger training:

Images Credit