After his suicide the body was taken outside the bunker, doused in fuel, set alight and then presumably hastily buried. The Soviets then took the area and recovered some remains, exactly how much is to this day unknown because the Soviets were not particularly forthcoming about it. What we do know is that part of the jaw was recovered, a part that included a dental bridge that could be identified by multiple sources as belonging to Hitler. There were probably other remains too that were used in the autopsy report that was eventually leaked to the west in the 60's. I say eventually because information about this is sketchy. It is possible that the extent of the remains recovered were exaggerated by the Soviets to lend further credence to the identification using the dental bridge. We know with reasonable certainty that more remains were uncovered, however, how useful they were is questionable since Hitler was cremated and buried along with Braun and two dogs.

The dental bridge was transported to the Soviet Union and it is still in Russia today. The rest of the remains were moved and reburied twice until they ended up under a red army base in East Germany. When control of the base was transfered from the Red Army to East Germany the remains were again exhumed, properly cremated and the ashes scattered in a river (specifically the Biederitz river) so that no remains were to be found.

All this said, we don't know exactly what happened because the SMERSH/KGB have not exactly been open about it. Various accounts have surfaced over the years with various stories about what happened to the remains. Some accounts state that the ashes were simply flushed down a toilet after cremation, others that they were scattered in the Biederitz river (a tributary to the Elbe which runs through Magdeburg).

We are fairly certain that in the 70's five boxes of human remains were exhumed and cremated. It is generally assumed that they contained the remains of Hitler, Braun, their dogs and the Göbbels family.