NASA's glorious shuttle program has come to an end.
The shuttle program was supposed to be an amazing success of American engineering, with as many as 50 launches per year, but in reality it fell far short of its goals. The same technology that was used for the space shuttles back in the sixties was used right up until the programs end. There was very little development under the control of the government.
Technology in the space shuttles has changed very little
The benefits of putting space travel in the hands of private corporations are numerous. One of the biggest benefits is the lack of red tape. Because NASA's shuttle program was under the control of the federal government, it took a long time to get funding and to make any changes because of all the bureaucracy that had to be waded through. Ideally, private companies would be able to make snap decisions and implement new techniques whenever it looked beneficial. Competition between companies would spur inovation on a level not possible for any government run organization. There would be strong motivations to progress, because these corporations would be in it for the money, whereas governments don't have such prerogatives.
SpaceX is a private space travel company
The idea for these many space industries is that they would ferry people to space for money. There are rocket/jet hybrids that are capable of taking people just above the Earth's atmosphere, these are largely what space industries are looking at in the near future. Eventually it is likely that these businesses will be able to take people to the moon and back, for a price. Once technology is advanced enough, it will become feasible for these companies to run successful businesses off of space travel.