Its still pretty sketchy. Mostly extrapolation from a line or two of dialog. From what we've seen cities like San Francisco and Paris seemed to survive with their landmarks intact. England seemed to make it through with its Royal institutions in place a well. The USA also made it through the war.
Star Trek future history has space exploration occurring while the war is going on. While some areas may have gone "Mad Max", there still seems to be an advanced technological society in others.