Well the short of it is... there was very little to find. The only remains which were absolutely verified as his were a piece of jaw bone and dental bridge, which were placed in a cigar box by the Soviets after finding them and having them identified. They were placed into storage in NVKD headquarters and remain there (or rather, now FSB) today. As for other remains, evidence is conflicting. The skull fragment some claimed was his has since been disproven, and the story that more remains existed which were buried in secret and then removed and burned in 1970 on orders of Brezhnev remain unsubstantiated. Quite possible it happened, but whether Hitler's remains actually existed with the other bodies is another matter. I go into a bit more detail on all of this here.

So the sum of it is, the only remains we absolutely know are Hitler's are probably in FSB headquarters. They might still be in a cigar box, but I'm inclined to believe they put them in a better container by now. Other remains might have existed, but if they did, they were cremated in secret in 1970.