Possibly the best book for you on this is Soldier Dead: How We Recover, Identify, Bury, and Honor Our Military Fallen by Michael Sledge. It's a well-written, comprehensive history from Columbia University Press and published in 2005.

Since I don't have a copy of that handy, I'll refer to the seventh volume of the mammoth Quartermaster Supply in the European Theater of Operations in World War II, which deals with the Graves Registration Service. Quartermaster Supply is the official history of the Quartermaster Corps in Europe during WWII and was first published in 1948.

In the U.S. Army, the Graves Registration Service or Graves Registration Division was slotted under the Quartermaster Corps. In Europe, it began operations on Dec. 9, 1941, when it began consulting with the British War Office regarding what to do with American military personnel who died in Northern Ireland, England, Wales and Scotland.

On the battlefield, which your question deals with, the official history states, "the collection, evacuation, and identification procedures which necessarily began on the battlefield were varied and to some extent improvised."

Soldiers who landed on Normandy, for example, learned only by experience how to handle bodies and remains. Their initial training had been that Graves Registration would handle all such matters.

Soon after the Normandy landings, this procedure was modified; bodies instead were delivered by combat units to a collection point near the battalion aid station, after which point the Graves Registration unit (typically a company in a division) would take over.

By the end of October 1944, the official history states, "the troops themselves actually preferred to evacuate and assist in the identification of their own comrades rather than leave them lying unattended in the fields to be picked up later."

In modern service, Sledge explains, there are several reasons for caring for the dead promptly. These include forensic reasons (if there is evidence of a war crime, that evidence must be examined promptly); health reasons (having human remains nearby is unhealthy); and psychological reasons.

Graves registration procedures developed rapidly in the American military after the Normandy landings, and by December 1944, the Third Army had summarized the reason why: "A positive identification was the last great service a combat unit could perform for its fallen comrades."