"Closed timelike curves" exist which are solutions to the General field equations. They've been known for some 70 years, and these space-time solutions do have a varying time axis. In short, time travel does exist in theory. Whether they actually exist in the real universe, in any useful sense is another question.
Future time travel is relatively easy, just go in the neighborhood of any heavy gravitational body - say, a black hole. Time slows down. Or travel close to the speed of light.
Personally I don't find time travel interesting anymore, other than future time travel.