Set in a pseudo timeless modern earth. There are no computers per-say, but some electronics in DMC2 more than likely.
There are only 2 "Worlds", the human realm and the demon realm.
Long ago the demon world gave rise to an emperor, who decided both worlds should become one. This led to an ensuing conflict, a very likely losing one between demons and humanity, with humans being overall disorganized and several others as those who bartered with demons for power.
Temen Ni Gru, one such hub for demon worshipping humans, built the place to ensure a gateway between the human and demon realms. Several other gateways were also being constructed.
However, one Demon saw beauty in the human world, and sought to preserve it. Upon seeing the destruction to the human world, and how innocents suffered at the hands of his demon comrades, one knight turned against his own. The Legendary Dark Knight, Sparda.
>Okay then what?
Somewhere after driving back so many demons, he came across a human woman, Eva, and was strangely captivated by her. Some sources might indicate Eva was the one who called upon him, but that's debatable.
Regardless, their union resulted in twin sons, Dante, and Vergil. Unfortunately for the family, Sparda's journey was not complete, some say he died, others say he vanished, but if anything else, he was not there to protect his family when the demons descended upon them.
>No shit.
Most of the lore I imagine can be found in enemy files, especially in 1 and 3. Perhaps a little bit of 4.