If you write the equations for the space around a black hole in the straightforward way you see a singularity at the event horizon. You can make a coordinate change that makes this singularity go away, but then you get the classical black hole singularity where there is either an "end of time" or an infinitely dense point or ring.
Physicists believed that this coordinate transformation was valid but it is not because it infinitely stretches space/time which at some point will blow up the Planck scale to be visible, at which point something completely indescribable happens -- it might be something like DSR or it might be different, but you void any warranty on the space time continuation, so the classical black hole is science fiction.
The obvious semiclasicalization is for the infinitely dense singularity to become a highly dense object which has some dimensions on the length of the Planck scale, but no model of quantum black hole using actual quantum gravity looks like that at all.
We don't have a "complete" theory of quantum gravity but we do have a number of competing partial theories, and we can already make some strong conclusions, such as holography, that are generic to many or any QG models. Underlying this are principles such as unitarity (unitarity is pretty much the one thing you need to make QM work) that means no information is lost when stuff falls in a black hole and that can't be reconciled with the mass being concentrated all in one place.