I'm not talking about survivors. They were obviously sent to a POW camp. Rather, I'm curious about how the bodies of allied aircrew made their way back to the U.S.
This is a good question. My answer deals largely with the Commonwealth experience in Northwest Europe here, with some passing references to Canadian forces, since that’s what I’m most familiar with.
To start, military authorities on both sides had an interest in crash sites for intelligence purposes (type of aircraft, armament and equipment carried, production data that could be inferred from serial numbers, etc.). Metal recycling was also a consideration, since aircraft could provide much-needed materials for the war effort. This was especially true for Germany as the war progressed. There was also the issue of making the crash sites safe, since they would sometimes contain UXO ranging from small arms ammunition to large bombs.
There would also be an interest in examining crash sites and surrounding areas because there was the possibility of survivors. They would be taken prisoner (or searched for if they were evading escape), and interrogated before being sent to POW camps. Towards the end of the war, some Allied flyers who survived being shot down were killed soon afterwards by German military personnel and/or civilians. There were postwar efforts to locate those responsible, some of which resulted in war crimes trials.
For much of the war, there were efforts made to recover and bury the remains of aircrew whose aircraft had crashed. Sometimes it was undertaken by military or police forces (including occupation forces in Occupied Europe), in other instances by civilians. Closer to the end of the war, or near the front lines, this was sometimes not possible due to the danger and general dislocation caused by ground combat, or by the deteriorating domestic conditions in Germany (or both).
The recovery of aircrew was complicated by the fact that aircraft crashes do horrific things to the human body. This includes high-speed impact, as well as fires and explosions caused by fuel and ammunition. In some cases, there were no easily identifiable remains to recover. In other cases, where aircraft with multiple crew members were involved, it sometimes wasn’t clear how many of the crew had been involved in the crash, or how many sets of remains had been recovered for burial. Burials took place in a variety of locations, sometimes near the crash site, but also in existing civilian or military cemeteries near the crash. In parts of Belgium and France, for instance, there are First World War cemeteries with a small number of Second World War burials, which are often of aircrew whose aircraft crashed in the area.
There were also some sites where there were no recovery efforts because the site was inaccessible, remained unknown, or was simply too remote. This was especially the case for aircraft that crashed into large bodies of water such as the English Channel or the North Sea, or into thinly-populated areas like mountains or deserts.
Formal notification of fatalities, and of personnel taken prisoner, took place through the International Committee of the Red Cross (ICRC). (The ICRC maintains the archives of POW files from both world wars and other conflicts, and these are accessible to research requests). German authorities would provide information to the ICRC, who would pass it along to Allied authorities, and vice versa — on the Western front, at least. (The Eastern front was another matter altogether, and there are other contributors far better placed to talk about it than I am.) Once this information was passed along, it was put to various uses by Allied authorities, including the notification of next of kin, but that’s a matter for a different discussion.
Notification, however, required that people on the ground know about the crash, and be able to identify and report the fatalities. Many of the issues mentioned above came into play here. In some instances, no information or only limited information could be provided. As a result, many aircrew remained officially missing, with death presumed to have happened after a set period of time if no further news was received.
Return of fatalities during the war wasn’t an option. Some repatriations of prisoners of war did take place. This usually consisted of personnel who were gravely ill or who had suffered serious injuries that rendered them unfit for further military service and who could not easily be cared for in POW camps.
As Allied forces advanced through formerly occupied areas, and through enemy territory, there were efforts to locate and confirm known burials (as reported through the ICRC, etc.), and to account for the missing.
Known, existing burials were relatively easy to register and deal with, but locating the missing was a significant challenge. For aircrew with the Royal Air Force (the British air force) and Commonwealth air forces associated with it (Royal Canadian Air Force, Royal Australian Air Force, Royal New Zealand Air Force, etc.) the primary way of doing this was through the Missing Research and Enquiry Service (MRES). Its task was to track down the roughly 42,000 Commonwealth air force personnel whose fates remained unknown. Drawing on whatever information had been gathered during the war (reports of crashes from other aircrew who returned and who were debriefed, fragments of information through the ICRC, etc.), they searched churchyards and cemeteries, spoke to local authorities and residents, and located and searched crash sites. Attempts to confirm the identity of burials often required the exhumation of wartime graves and the use of remaining clues that included hair colour, dental work, details of uniforms, names on clothing, or other personal effects. These efforts continued until 1952.
Burials located in the process were often relocated to other cemeteries. For the Commonwealth examples mentioned above, this would usually be a Commonwealth War Graves Commission (CWGC) cemetery at a designated location. (At the time of these events, it was still the Imperial War Graves Commission; its name changed in the 1960s.) In other instances, burials remained in local cemeteries, but their care became the responsibility of the CWGC. In some cases, the MRES efforts (and efforts of other graves registration personnel) resulted in individual identified burials. In others, where only the collective identity of a crew (or several of its members) could be established, collective burials were made, with a headstone or headstones engraved with multiple names, as appropriate. The reburial and marking of graves also held true for those who could be partially identified (e.g. a Flight Lieutenant in the RCAF), but whose names could not. For those who remained missing, various memorials — most notably the Air Forces Memorial at Runnymede - were built to record their names.
It’s worth noting that for CWGC burials repatriation of remains from foreign countries for burial at home was not an option, which is a significant difference from American practice following both world wars. With luck, someone will comment on the American experience — I’m familiar with its general outlines, but not its details.
The most accessible source I can recommend for this is Stuart Hadaway’s Missing Believed Killed: Casualty Policy and the Missing Research Enquiry Service 1939-1952, (Pen and Sword, various editions), ISBN 978-1848846593.
I can also suggest the Hubert Brooks website — Brooks was a Canadian pilot with a fascinating wartime career; he was shot down, evaded capture, and fought with the Polish Home Army. He was also a member of the RCAF Flyers who won the 1948 Olympic hockey gold medal. For a number of years, he also served in the MRES, and a section of the website covers this. There’s also a first-hand account by Duncan Torrance on the BBC’s archived WW2 People’s War website that gives some insight into the challenges of MRES and graves registration work and related duties in Northwest Europe immediately after the war. The most relevant material starts in Chapter 15a “Back to Exhumations and Crosses”.
Hope this helps!