His was father was Macedonian, not Greek; his mother was from Greek tribe in Epirus (modern Albania), and her mother was supposedly from the Troad. Alexander cut a wide swath with women, although this gay BS pops up (ahem) every so often. It's a juicy **** sandwich. There's also been a book claiming he was an alcoholic, which probably wasn't true, but at least that one is plausible. :^)
Alexander had to figure out how to cope with an army in India which used elephants as tanks, and also sneak his entire army across a river in the night, without boats, in order to get in place to fight the battle. His method of dealing with elephants was taught in military schools for the rest of antiquity. The Romans used it so effectively that the last major use of elephants in the Med basin was the Battle of Thapsus, which ended most of the thugs fighting Julius Caesar.
Olympias was Molossian. Epirus corresponds partly to what is the extreme northwestern part of Greece (opposite Corfu) and partly the nearby part of Albania, but the Molossi appear to have been in the area that now belongs to Greece.