Expeditionary warfare
In the ancient world: The earliest examples of expeditionary warfare come from the Sea Peoples, a term used for a confederation of seafaring raiders of the second millennium BC who sailed into the eastern shores of the Mediterranean, caused political unrest, and attempted to enter or control Egyptian territory during the late 19th dynasty, and especially during Year 8 of Ramesses III of the 20th dynasty.

The raiding tactics were expanded into the more complex expeditionary warfare operations by Alexander the Great who used naval vessels for both troop transporting and logistics in his campaigns against the Persian Empire.
The next exponents of expeditionary warfare in the ancient world of the Mediterranean Basin were the Carthaginians who introduced two entirely new dimensions to the use of naval forces by staging not only operations that combined naval and land troops, but also eventuated in combining strategic multi-national forces during the land phase of the operation when Hannibal in his most famous achievement at the outbreak of the Second Punic War marched an army, which included war elephants, from Iberia over the Pyrenees and the Alps into Northern Italy.
Following on the example of Carthage, the Romans used expeditionary operations extensively to expand their Empire and influence in the Mediterranean and beyond, including the Roman conquest of Britain which was not only a limited expeditionary operation, but one conceived to include long-term occupation and Roman settlement of the territories.

The Han dynasty of ancient China also famously used expeditionary warfare to deal with the nomadic Xiongnu people during the Han–Xiongnu War. Under the orders of Emperor Wu of Han, the Han launched numerous long-distance raids deep into Xiongnu territory. The exploits of famed Han generals Wei Qing and Huo Qubing were of particular note, with both recording multiple successful expeditions between the years 127 and 119 BC, eventually annexing the Hexi Corridor and expelling the Xiongnu from the Qilian Mountains. The expeditionary Han forces were primarily made up of cavalry and were typically arrayed in columns. They also frequently crossed vast distances–Huo Qubing is said to have travelled 2,000 li, roughly 620 miles, during one of his raids.

In the Middle Ages: Shortly after the collapse of the Roman empire in Italy, the European Middle Ages began with an expedition of imperial Byzantine general Belisarius against the Vandals. But as that empire dwindled, its warfare became more defensive.
The most prominent development of expeditionary warfare during the Middle Ages came from the environmental pressures in the Scandinavian region during the Middle Ages, and the emergence of the Viking migrations that combined raiding, longer term inland operations, occupation and settlement. These operations were conducted as sea, coastal and riverine operations, and sometimes were strategic in nature, reaching as far as Constantinople.
Expeditionary warfare in East Asia began very much in the same way it had in the Mediterranean with short-term raids by Japanese pirates. Because the wokou were weakly resisted by the Ming dynasty, the raiding eventually developed into fully-fledged expeditionary warfare with the Japanese invasions of Korea (1592–1598).

During the Crusades: The development in expeditionary operations reached a new level when during the Crusades the element of political alliance as an influence on the military strategy was introduced, for example in the Sixth Crusade (AD 1228.)

The rise of European colonial empires: Although all expeditionary warfare until the invention of the combustion engine was largely dependent on sailing vessels, it was with the creation of sophisticated rigging systems of the European Renaissance that the Age of Sail allowed a significant expansion in expeditionary warfare, notably by the European colonial empires. Some have argued that this was the first revolution in military affairs that changed national strategies, operational methods, and tactics both at sea and on the land. One notable example of this evolution was the French invasion of Egypt (1798).
Though a significantly expanded expeditionary operation, the Crimean War was the first example of a planned expeditionary campaign that was directed as part of a multinational coalition strategy. It was also the first modern expeditionary operation that used steam-powered warships and telegraph communications.
The next development in the evolution of the expeditionary warfare was made during the expansion of the western European empires and the era of colonialism that also led to the inclusion of the expeditionary methods into the direct expression of national strategies to avoid full-scale conflicts in the shape of the gunboat diplomacy approach. It was at this time that naval troops previously used almost exclusively for defence of vessels or minor beach operations were expanded to enable extended littoral operations. The colonial experience, though largely confined to the period before the First World War, persisted well into the 20th century.

The World Wars: 

First World War: The period of the First World War and its aftermath in the 1920s saw expeditionary warfare established as a systematic and planned type of operations with larger scope than simple transportations of troops to the theatre, such as the British Expeditionary Force in 1914, Russian Expeditionary Force in 1916, and the American Expeditionary Forces in 1917, and the beginnings of development in true combined operations at strategic, operational and tactical levels with the unsuccessful amphibious landing at Gallipoli. Not only did this operation combine the elements of overall war planning context, multinational deployment of forces as part of the same operation, and use of troops prepared for the landings (as opposed to disembarkation), as well as naval gunfire support that was limited during the era of sailing ships, but also included extensive use of combat engineering in support of the infantry. One of the most extensive and complex of expeditionary operations that followed the war was the Allied intervention in the Russian Civil War that saw forces deployed in the Baltic region, the Arctic region, along the Black Sea coast, and in the Russian Far East.

Other expeditionary forces during WWI included:

Canadian Expeditionary Force 1914–1920
First Australian Imperial Force (Europe)
Indian Expeditionary Force 1914–1918
Hejaz Expeditionary Force (Ottoman Empire) 1916-1919
South African Overseas Expeditionary Force 1915–1919
New Zealand Expeditionary Force 1914–1918
Portuguese Expeditionary Corps 1917–1918

Second World War: Afrika Korps (Nazi Germany)
Corpo Aereo Italiano (Fascist Italy)
Corpo Truppe Volontarie
Brazilian Expeditionary Force
British Expeditionary Force
Canadian Corps
China Expeditionary Army (Imperial Japan)
Chinese Expeditionary Force (Chinese Army)
Italian Expeditionary Corps in Russia
Second Australian Imperial Force

Contemporary: 

European Union: EU Battlegroup
European Maritime Force

NATO: NATO Response Force
Allied Rapid Reaction Corps

United Kingdom: 3rd Division (United Kingdom)
16 Air Assault Brigade
3 Commando Brigade
Joint Expeditionary Force (Maritime)
Joint Expeditionary Force
Combined Joint Expeditionary Force
Joint Rapid Reaction Force
No. 83 Expeditionary Air Group
No. 901 Expeditionary Air Wing
No. 902 Expeditionary Air Wing
No. 903 Expeditionary Air Wing
No. 904 Expeditionary Air Wing
No. 906 Expeditionary Air Wing
Expeditionary Air Wing
No. 34 Expeditionary Air Wing
No. 38 Expeditionary Air Wing
No. 121 Expeditionary Air Wing
No. 135 Expeditionary Air Wing
No. 138 Expeditionary Air Wing
No. 140 Expeditionary Air Wing

United States: Carrier Strike Group
Carrier Strike Group 1
Carrier Strike Group 2
Carrier Strike Group 3
Carrier Strike Group 5
Carrier Strike Group 8
Carrier Strike Group 9
Carrier Strike Group 10
Carrier Strike Group 11
Carrier Strike Group 12

Navy Expeditionary Combat Command
Expeditionary Strike Group
Marine Expeditionary Force
I Marine Expeditionary Force
II Marine Expeditionary Force
III Marine Expeditionary Force
Marine Expeditionary Brigade
1st Marine Expeditionary Brigade
2nd Marine Expeditionary Brigade
3rd Marine Expeditionary Brigade
Marine Expeditionary Unit
11th Marine Expeditionary Unit
13th Marine Expeditionary Unit
15th Marine Expeditionary Unit
22nd Marine Expeditionary Unit
24th Marine Expeditionary Unit
26th Marine Expeditionary Unit
31st Marine Expeditionary Unit
List of Air Expeditionary units of the United States Air Force (43 of them)

See also: Blue-water navy
Expeditionary energy economics
Expeditionary maneuver warfare
Loss of Strength Gradient
Military deployment
Military logistics
Over-the-beach capability
Power projection
Seabasing
Unsinkable aircraft carrier

References: 

External links: Response Force Task Group (RFTG) (Royal Navy PDF)