Up until World War I (except for some experimentation with division and corps structures during the Civil War), the US Army was organized mostly by regiments and brigades. When we entered World War I, we started forming divisions in order to match up with the structures and employment of European armies. A division consists of about ten to twenty thousand soldiers organized into several brigades plus auxiliary units, and is presently the smallest unit able to operate completely independently in the field. There is currently a move on to go back to the old brigade structure in place of divisions.
First Infantry Division is of course the first, and was organized out of existing army brigades upon our entry into World War I in 1917. It has seen continuous service since then. Current home base is Fort Riley, Kansas
World War I (Cantigny, Soissons, St. Mihiel, Argonne Forest)
World War II (North Africa, Sicily, D-Day, Battle of the Bulge)
Vietnam
First Gulf War
Kosovo
Second Gulf War