Yes, we have the theory of what is required to build one but every material we have (including graphene and carbon nanotubes) is about 2-3 orders of magnitude below the tensile strength that is required for a space elevator on earth. Add in the fact that the longest graphene and carbon nanotube we can currently produce is in the mm range and we need it to be ~50,000 km and perfect at the atomic level we would be at best decades away from production if they could be used.

Ironically the best place for us to begin is in space.

Building space elevator on the moon is much, much easier (1/6 G and no atmosphere) and Mars is also a much easier proposition than on earth (1/3 G and 1/1000th the atmospheric pressure).

I fully expect that if humans ever build space elevators the first one will not be on earth.