'None. Stephen Hawking is overrated.'
Err no. Unfortunately Hawkings isn't up to date with some of the quantum theories of gravity floating around, so his solution will probably be classical, however he is also one of the foremost experts on the subject in the world. His reputation precedes him, he's been right a number of times, and well everyone is kinda interested in the specifics (that will be revealed at a conference next week).
The field is actually getting a surge of interest in the last few months, and everyone seems to have a different pet solution.
Essentially the problem is the following. Evolve a quantum state that is by nature a unitary process, and collapse it into a blackhole. Eventually the black hole will evaporate by well known processes that Hawkings discovered back in the 70s. The outgoing state is now thermal and mixed. Quantum mechanics says that you can't evolve a quantum state into a mixed state. What happened?
Up until recently, people have sorta assumed that this was essentially unsolvable unless you had a correct theory of the microscopics of the affair, read a quantum theory of gravity. There were several papers by string theorists that claimed to have resolved the process.
What will be interesting is seeing how all these competing theories actually mix and match (or not at all). The problem is, in principle, measurable so one day we will now.