Are all the Black Ops games connected? Technically, they all take place on Earth in the same universe within the Virgo supercluster of galaxies... That said, the games aren't really connected story/campaign-wise, except for the 3 original Modern Warfare games.
Call of Duty: Black Ops III takes place in 2065, 40 years after the events of Black Ops II, in a world facing upheaval from conflicts, climate change and new technologies. A Third Cold War is ongoing between two global alliances, known as the Winslow Accord and the Common Defense Pact.