Circumvallation
Antiquity: Thucydides notes the role circumvallation played in the Sicilian Expedition and in the Spartan siege of Plataea during the initial stages of the Peloponnesian War in 429 BC.
Julius Caesar in his Commentaries on the Gallic War describes his textbook use of the circumvallation to defeat the Gauls under their chieftain, Vercingetorix, at the Siege of Alesia in September 52 BC.
During the Siege of Jerusalem, Titus and his Roman legions built a circumvallation, cutting down all trees within fifteen kilometres (9 miles).

Middle Ages: Another example from the pre-modern period is the Siege of Constantinople (717–718).
The caliph of the Umayyad Empire took advantage of the violent anarchy in the Byzantine Empire to prepare a huge host, comprising more than 100,000 troops and 1,800 ships, to take them to the Byzantine capital, Constantinople. Upon arriving outside the city's Theodosian walls, the Arab army had some knowledge that Emperor Leo III the Isaurian had allied with Bulgaria under Khan Tervel, and so, in preparation for the Bulgarian army, built a set of stone walls against the city and against the countryside, with the Arab camp in between.
King Pepin the Short of Francia built a number of fortified camps during his Siege of Bourbon (761) to surround the town completely. He built a complete set of lines of circumvallation and contravallation during the Siege of Bourges (762).

Modern era: The basic objectives and tactics of a military investment have remained the same in the modern era. During the Second World War, there were many sieges and many investments. One of the best-known sieges of the war, which demonstrated the tactical use of investment, was the 
Siege of Stalingrad. During the first half of the siege, the Germans were unable to fully encircle the city and so the Soviets got men and supplies in across the Volga River. During the second half of the battle, the complete investment of Stalingrad by the Soviets, including airspace, which prevented the construction by the Germans of an adequately large airbridge, eventually forced the starving Germans in the city to surrender.
In modern times, investments and sieges of cities are often combined with intensive shelling, air strikes and extensive use of land and/or sea mines.

See also: Encirclement
List of established military terms

References: 

Sources: Petersen, Leif Inge Ree (2013). Siege Warfare and Military Organization in the Successor States (400–800 AD): Byzantium, the West and Islam. Leiden: Brill. ISBN 978-90-04-25199-1.