Airborne forces
Early history: Benjamin Franklin envisioned the danger of airborne attack in 1784, only a few months after the first manned flight in a hot air balloon:

Five Thousand Balloons capable of raising two Men each, would not cost more than Five Ships of the Line: And where is the Prince who can afford so to cover his Country with Troops for its Defense, as that Ten Thousand Men descending from the Clouds, might not in many Places do an infinite deal of Mischief, before a Force could be brought together to repel them?
An early modern operation was first envisioned by Winston Churchill who proposed the creation of an airborne force to assault behind the German lines in 1917 during the First World War. Later in late 1918. Major Lewis H. Brereton and his superior Brigadier General Billy Mitchell suggested dropping elements of the U.S. 1st Division behind German lines near Metz. The operation was planned for February 1919 but the war ended before the attack could be seriously planned. Mitchell conceived that US troops could be rapidly trained to utilize parachutes and drop from converted bombers to land behind Metz in synchronisation with a planned infantry offensive.
Following the war, the United States Army Air Service experimented with the concept of carrying troops on the wings of aircraft, with them pulled off by the opening of their parachutes. The first true paratroop drop was by Italy in November 1927. Within a few years, several battalions were raised and eventually formed into two Folgore and Nembo divisions. Although they later fought with distinction in World War II, they were never used in a parachute drop. Men drawn from the Italian parachute forces were dropped in a special-forces operation in North Africa in 1943 in an attempt to destroy parked aircraft of the United States Army Air Forces.
At about the same time, the Soviet Union was also experimenting with the idea, planning to drop entire units complete with vehicles and light tanks. To help train enough experienced jumpers, parachute clubs were organized with the aim of transferring into the armed forces if needed. Planning progressed to the point that Corps-size drops were demonstrated to foreign observers, including the British Military Attaché Archibald Wavell, in the Kiev military district maneuvers of 1935.
One of the observing parties, Nazi Germany, was particularly interested. In 1936, Major F. W. Immans was ordered to set up a parachute school at Stendal (Borstel), and was allocated a number of Junkers Ju 52 aircraft to train on. The military had already purchased large numbers of Junkers Ju 52s which were slightly modified for use as paratroop transports in addition to their other duties. The first training class was known as Ausbildungskommando Immans. They commenced the first course on May 3, 1936.
Other nations, including Argentina, Peru, Japan, France and Poland also organized airborne units around this time. France became the first nation to organize women in an airborne unit, recruiting 200 nurses who during peacetime would parachute into natural disaster zones but also as reservists who would be a uniformed medical unit during wartime.

World War II: 

Axis operations: Several groups within the German armed forces attempted to raise their own paratroop formations, resulting in confusion. As a result, Luftwaffe General Kurt Student was put in overall command of developing a paratrooper force to be known as the Fallschirmjäger.
During the invasions of Norway and Denmark in Operation Weserübung, the Luftwaffe dropped paratroopers on several locations. In Denmark, a small unit dropped on the Masnedøfort on the small island of Masnedø to seize the Storstrøm Bridge linking the islands of Falster and Zealand. A paratroop detachment also dropped at the airfield of Aalborg which was crucial for the Luftwaffe for operations over Norway. In Norway, a company of paratroopers dropped at Oslo's undefended airstrip. Over the course of the morning and early afternoon of April 9, 1940, the Germans flew in sufficient reinforcements to move into the capital in the afternoon, but by that time the Norwegian government had fled.
In the Battle of France, members of the Brandenburg Regiment landed by Fieseler Fi 156 Storch light reconnaissance planes on the bridges immediately to the south of the 10th Panzer Division's route of march through the southern Ardennes. In Belgium, a small group of German glider-borne troops landed on top of the Belgian fortress of Eben Emael on the morning of May 10, 1940, and disabled the majority of its artillery. The fort held on for another day before surrendering. This opened up Belgium to attack by German Army Group B.
The Dutch were exposed to the first large scale airborne attack in history. During the invasion of the Netherlands, the Germans threw into battle almost their entire Luftlandekorps, an airborne assault army corps that consisted of one parachute division and one division of airlanding troops plus the necessary transport capacity. The existence of this formation had been carefully kept secret until then. Two simultaneous airborne operations were launched. German paratroopers landed at three airfields near The Hague, hoping to seize the Dutch government. From one of these airfields, they were driven out after the first wave of reinforcements, brought in by Ju 52s, was annihilated by anti-aircraft fire and fierce resistance by some remaining Dutch defenders. As a result, numerous crashed and burning aircraft blocked the runway, preventing further reinforcements from landing. This was one of the few occasions where an airfield captured by paratroops has been recaptured. The other two airfields were recaptured as well. Simultaneously, the Germans dropped small packets of paratroopers to seize the crucial bridges that led directly across the Netherlands and into the heart of the country. They opened the way for the 9th Panzer Division. Within a day, the Dutch position became hopeless. Nevertheless, Dutch forces inflicted high losses on German transportation aircraft. Moreover, 1200 German elite troops from the Luftlandekorps taken prisoner around The Hague, were shipped to England just before the capitulation of the Dutch armed forces.
The Fallschirmjägers' greatest victory and greatest losses occurred during the Battle of Crete. Signals intelligence, in the form of Ultra, enabled the British to wait on each German drop zone, yet despite compromised secrecy, surviving German paratroops and airlanded mountain troops pushed the Commonwealth forces off the island in part by unexpected fire support from their light 75 mm guns, though seaborne reinforcements were destroyed by the Royal Navy. However, the losses were so great that Adolf Hitler forbade their use in such operations in the future. He felt that the main strength of the paratroopers was novelty, and now that the British had clearly figured out how to defend against them, there was no real point to using them any more.
One notable exception was the use of airborne forces in special operations. On September 12, 1943, Otto Skorzeny led a daring glider-based assault on the Gran Sasso Hotel, high in the Apennines mountains, and rescued Benito Mussolini from house arrest with very few shots being fired. On May 25, 1944, paratroopers were dropped as part of a failed attempt to capture Josip Broz Tito, the head of the Yugoslav Partisans and later postwar leader of Yugoslavia.
Before the Pacific War began, the Imperial Japanese Army formed Teishin Dan ("Raiding Brigades") and the Imperial Japanese Navy trained marine (Rikusentai) paratroopers. They used paratroops in several battles in the Dutch East Indies campaign of 1941–1942.
Rikusentai airborne troops were first dropped at the Battle of Manado, Celebes in January 1942, and then near Usua, during the Timor campaign, in February 1942. Teishin made a jump at the Battle of Palembang, on Sumatra in February 1942. Japanese airborne units suffered heavy casualties during the Dutch East Indies campaign, and were rarely used as parachute troops afterward.
On 6 December 1944, a 750-strong detachment from Teishin Shudan ("Raiding Division") and the Takachiho special forces unit, attacked U.S. airbases in the Burauen area on Leyte, in the Philippines. The force destroyed some planes and inflicted casualties, but was eventually wiped out.
Japan built a combat strike force of 825 gliders but never committed it to battle.

Allied operations: Ironically, the battle that ended Germany's paratrooper operations had the opposite effect on the Allies. Convinced of the effectiveness of airborne assaults after Crete, the Allies hurried to train and organize their own airborne units. The British established No.1 Parachute Training School at RAF Ringway near Manchester, which trained all 60,000 European paratroopers recruited by the Allies during World War II.
An Airlanding School was also set up in New Delhi, India, in October/November 1941, at the then-Welllingdon Airport (now the defunct Safdarjang Airport) to train paratroopers for the British Indian Army which had been authorised to raise an airborne-capable formation earlier, resulting in the formation of the 50th Indian Parachute Brigade.