In this system, regiments are simply there to preserve units' lineage, and few regiments actually are combat bodies (in the United States Army, there are very few remaining infantry, cavalry, or artillery regimental bodies). The exceptions remain the "special" units, such as engineer regiments. Rather, the regiments are split into battalions (infantry, usually three) or squadrons (cavalry, usually three or more). Artillery can be split into battalions, batteries, or other units, depending on the type. These battalions are the actual combat units. For example, West Point is garrisoned by the 1st Battalion, 1st Infantry. However, the actual unit, the "1st Infantry", technically does not exist in military unit terms.
This system has been adopted only recently (about 1953) by the U.S. Army. Before then, it used the traditional regimental system, where regiments were actual combat units. This change can be viewed in the following examples:
(This is just a fictional example)
(This is just a fictional example)
Order of Battle: 1860 US Army
Order of Battle: 2000 US Army