Well we can already build them on the moon or mars, but there's not much use to do that at this point. The physics of a space elevator our completely understood, it's "just" finding a strong enough material to build the tether. A star trek transporter is still far out of reach.
The physics of rockets is completely understood, too, and several applications have already been debugged. It's "just" a matter of finding a better propellent.
