In the United States and other armies, it refers to a unit of approximately 30,000 troops, composed of two or more divisionss, and typically commanded by a lieutenant general.
As of 2003, the United States Army has four corps. The structure of a corps is not permanent; many of the units that it commands are allocated to it as needed on an ad hoc basis. On the battlefield, the corps is the highest level of the forces that is concerned with actually fighting and winning the war. (Higher levels of command are concerned with administration rather than fighting, at least in current doctrine.) The corps provides operational direction for the forces under its command. Corps are designated by consecutive Roman numerals. The present active corps in the US Army are I Corps ("eye core"), III Corps, V Corps, and XVIII Airborne Corps; their numbers derive from four of the 30-odd corps that were formed during WWII.
In the British Army, a corps tends to be a grouping by common function (eg, the Infantry corps, the Royal Logistics Corps, Royal Corps of Signals). There is a corps headquarters for operational control of forces, and it was last deployed as the headquarters commanding land forces during the Kosovo War in 1999. Other than that, a British corps headquarters has not deployed in the field since 1945.
In Germany, German Student Corps are a unique kind of studenten corporation similar to fraternities elsewhere, proud about democracy, tolerance and the German vaterland. These corps originated in the late 18th century.
See also: corps area, United States Marine Corps, List of corps of the United States Army