Partial Space Elevator
Don't tether the Earth-facing end of space elevator: let it hang in the atmosphere, and arrive to it with less fuel.
The idea of space elevator is not new at all, but the consideration of not tethering one of its ends to Earth has not been widely discussed.
It's not new though: a paper of 2014 from Acta Astronautica has analyzed the idea of a space elevator with both of its ends hanging in space, and found that it might cut the costs of space travel to high orbit by 40 percent.
I think it's worth putting this idea down here, so that relevant projects could be linked to it in the future.
+[project]
Two points:
We can start rolling out the lightest part of it - the tip - right now! The strength required by the tether is not the same across its length - to minimize weight, it has to be tapering off towards the Earth's end, with very light tip. So, let's find a suitable geostationary sattelite in orbit already, and bring some tape (tether) to it.
Space junk that's already in orbit, is great for the counterweight construction. It requires much less fuel to lift the junk into the geostationary orbit, than to lift it up from Earth surface.