Airborne operation
Burma: A large British force, known as the Chindits, operated behind Japanese lines during 1944. In Operation Thursday, most of the units were flown into landing grounds which had been seized by glider infantry transported by the American First Air Commando Group, commencing on March 5. Aircraft continued to land reinforcements at captured or hastily constructed landing strips until monsoon rains made them unusable. Small detachments were subsequently landed by parachute. The operation eventually wound down in July, with the exhausted Chindits making their way overland to link up with advancing American and Chinese forces.
For Operation Dracula, an ad hoc parachute battalion group made up of personnel from the 153 and 154 (Gurkha) Parachute Battalions of the Indian Army secured Japanese coastal defences, which enabled the seaborne assault by the 26th Indian Infantry Division to attain its objectives with a minimum of casualties and time.

Ecuadorian–Peruvian War: During the Ecuadorian–Peruvian War, the Peruvian army established its own paratrooper unit and used it to great effect by seizing the Ecuadorian port city of Puerto Bolívar, on July 27, 1941, marking the first time in the Americas that airborne troops were used in combat.

After World War II: 

Indonesian War of Independence: The Dutch Korps Speciale Troepen made two combat jumps during the Indonesian War of Independence. The first jump was as part of Operation Kraai: the capture of Yogyakarta, and the capture of Sukarno and Mohammad Hatta on 19 and 20 December 1948. 
The second combat jump happened during Operation Ekster: the capture of Jambi and the oilfields surrounding is, on Sumatra from 29 December 1948 to 23 January 1949. From the Indonesian side, the first airborne operation was an airborne-infiltration operation by 14 paratroopers on 17 October 1947, in Kotawaringin, Kalimantan.

Korean War: The 187th Airborne Regimental Combat Team ("Rakkasans") made two combat jumps in Korea during the Korean War. The first combat jump was made on October 20, 1950, at Sunchon and Sukchon, North Korea. The missions of the 187th were to cut the road north going to China, preventing North Korean leaders from escaping from Pyongyang; and to rescue American prisoners of war.
The second combat jump was made on Wednesday, March 21, 1951, at Munsan-ni, South Korea codenamed Operation Tomahawk. The mission was to get behind Chinese forces and block their movement north. The Indian Army 60th Parachute Field Ambulance provided the medical cover for the operations, dropping an ADS and a surgical team totalling 7 officers and 5 other ranks, treating over 400 battle casualties apart from the civilian casualties that formed the core of their objective as the unit was on a humanitarian mission. The unit was to become the longest-serving military unit in any UN operation till date, serving from October 1950 till May 1953, a total of three and a half years, returning home to a heroes' welcome.
The 187th served in six campaigns in Korea. Shortly after the war the 187th ARCT was considered for use in an Airborne drop to relieve the surrounded French garrison at Dien Bien Phu in Vietnam but the United States, at that time, decided not to send its troops into the combat zone.
The unit was assigned to the reactivated 101st Airborne Division and subsequently inactivated as a combat team in 1956 as part of the division's reorganization into the Pentomic structure, which featured battle groups in place of regiments and battalions. The 1st and 3rd Battalions, 187th Infantry, bearing the lineages of the former Co A and Co C, 187AIR, are now with the 101st Airborne Division as air assault units.

First Indochina War: The French used paratroopers extensively during their 1946-54 war against the Viet Minh. Troupes de marine, Foreign Legion and local Vietnamese units took part in numerous operations which were to culminate in the disastrous siege of Dien Bien Phu.

Suez crisis: Operations Machbesh & Musketeer: Launching the 1956 Suez War, on October 29, 1956, Israeli paratroopers led by Ariel Sharon dropped onto the important Mitla Pass to cut off and engage Egyptian forces. Operation Machbesh (Press) was the IDF's first and largest combat parachute drop.
A few days later, Operation Musketeer needed the element of total surprise to succeed, and all 660 men had to be on the ground at El Gamil airfield and ready for action within four and a half minutes. At 04.15 hours on November 5, 1956, British 3rd Battalion, Parachute Regiment jumped in and although opposition was heavy, casualties were few. Meanwhile, French paratroopers of the 2nd Marine Infantry Parachute Regiment under the command of Colonel Chateau-Jobert jumped on the water treatment factory South of Port Said.
The landings from the sea the next day saw the first large-scale heliborne assault, as 45 Commando, Royal Marines were landed by helicopters in Port Said from ships offshore. Both the British and the French accomplished total military victory against the disorganized Egyptian military and local armed civilians but political events forced total retreat of these forces after 48 hours of fighting.

Indo-Pakistani War of 1965: Paratroopers were used in combat in South Asia after the Second World War during the Indo-Pakistan War of 1947, Indian Annexation of Goa in 1961 and Indo-Pakistani War of 1965. The war in 1965 had the largest use of paratrooper forces, and unlike in previous conflicts, they were used in their intended capacity fully (They were not used in the airborne capacity in 1961, and it is unconfirmed in 1947). A covert operation was launched by the Pakistani Army with the intention of infiltrating Indian airbases and sabotaging them. The SSG (Special Service Group) commandos, were parachuted into Indian territory. Of the 180 para-commandos dropped, 138, including all officers but one, were captured and safely taken to prisoner of war (POW) camps. Twenty-two were killed, or rather lynched by joint combing teams of villagers armed with sticks, police and even bands of muleteers released by the Army, from the animal transport battalion of the nearby Corps headquarters.
Only 20 para-commandos were unaccounted for and most escaped back to Pakistan under the fog. Most of these were from the Pathankot group, dropped less than 10 km from the border in an area that had plenty of ravines, riverine tracks to navigate back along.
The War also saw the establishment of the first Indian Airborne Special Forces Unit - The Meghdoot Force - which was tasked with operations behind Pakistani Lines. This force is the predecessor to the modern India Para commando (SF) units, and had a major influence on modern Indian Special forces units.

Bangladesh Liberation War of 1971: During the Bangladesh Liberation War of 1971, the Parachute Regiment of the Indian Army fought in numerous contacts in both the Eastern and Western Theatres. On 11 December, India airdropped the 2nd battalion (2 Para) in what is now famous as the Tangail airdrop. The paratroop unit was instrumental in denying the retreat and regrouping of the Pakistani Army and contributed substantially to the early collapse of Dhaka via covert operations. The regiment earned the battle honours of Poongli Bridge, Chachro and Defence of Poonch—during these operations.

Indonesian Invasion of East Timor: The Indonesian Army used airborne troops in their 1975 invasion of East Timor. Following a naval bombardment of Dili, on December 7, 1975, Indonesian seaborne troops landed in the city while paratroops simultaneously descended on the city. 641 Indonesian paratroopers jumped into Dili, where they engaged in six-hours combat with East Timorese gunmen.

Vietnam War: In 1963, in the Battle of Ap Bac, ARVN forces delivered airborne troops by helicopter and air drop. The use of helicopter-borne airmobile troops by the United States Army in the Vietnam War was widespread, and became an iconic image featuring in newsreels and movies about the conflict.
In February 1967 Operation Junction City was launched, it would be the largest operation the Allied forces would assemble. During this operation, 845 members of the 2nd Battalion, 503rd Airmen (Airborne), the 319th Artillery (Airborne), and elements of H&H company of the 173rd Airborne Brigade made the only combat jump in Vietnam.

Rhodesian Bush War: The men of the Rhodesian Light Infantry made more parachute jumps than any other military unit in history. While an Allied paratrooper of the Second World War would be considered a "veteran" after one operational jump, an RLI paratrooper could make three operational jumps in a single day, each in a different location, and each preceding a successful contact with the enemy. Between 1976 and 1980, over 14,000 jumps were recorded by the Rhodesian Security Forces as a whole.