The Jeff Bezos side of the Musk/Bezos Space Race
Mr. Musk's contribution:
McDonnell Douglas and NASA were futzing with this sort of thing back in the 90s, in the form of the Delta Clipper:
Sadly, it never really got off the ground.
(Bezos' and Musk's efforts found at SondraKistan)
If you want to get an idea of the technologies involved in this kind of project, check out the job listings at Blue Origin!