Time travel is the concept of moving through it as though it were a spatial, rather than a temporal, dimension.
The concept has intrigued humanity for many centuries, ever since the genre of science fiction was created, humans dreamed of moving through time. The first attempt was nothing more than the first interstellar flight in 2057 during the bullet mission. It was a simple experiment with time dilation.
The next test was to launch a probe to orbit Bartman's Star (a black hole relatively close to Earth) in 2139. It came back in 2142 to show that only a few minutes had passed while it was close to the black hole. Some of the more rich and famous people chose this method to stay alive a lot longer and this technique was used to extend the lives of terminal patients so that their doctors could try and work on a cure for their disease.
While travel to the future (in a sense) was possible, travel to the past was much harder to figure out. The only experiment to attempt this destroyed an entire planet in 2421. With this, the URSS banned the experimentation of travel to the past, not just because of the destruction but because of the fear of changing the past. When the Confederacy took power they lifted the ban but no one has attempted to travel to the past.
Travel to the future is still in practice, mostly by terminally ill patients, people looking to extend their own lives and/or watch the human race expand (See: Traveler), and criminals looking to escape their captors.
Time travel has always been an incredibly dangerous practice around some black holes because of Black Hole Induced Psychosis. Anomalous black holes that cause BHIP are not to be approached under any circumstances for time travel experiments.