Ah. Good question. Things probably started diverging a little in the 1800s, but there were only minor changes until World War II, which ended in a distinct lack of nuclear hellfire. Still, the US and the USSR became rival superpowers with the war's aftermath, and their game was played similarly to OTL. The big postwar difference was that Africa diverged greatly from OTL after decolonization, with a key change being that not many in Africa thought the old colonial borders were particularly valid. The specifics of this I'll leave to D'Art, Kraznaya, and anyone else who wants to take a nation on the continent. Too, Indonesia might have gone for a monarchy in the immediate post-war period, but I'll leave this fuzzy in case someone takes the country.
Aside from Africa, major changes didn't start to take place until the Berlin Wall came down. The Soviet and European disorder led to disorder in North America, which led to disorder in both Asia and South America. The world kind of dominoed in the 1990s, and it is important to remember that until that decade, the world map was almost exactly OTL's. (With the exception of Africa, again.)
EDIT: Also, as this preview thread is moving away from its original purpose, here's a reminder that I'm still accepting reservations.