Time travel is the concept of moving either forward or backwards in two points in time as if the two points were like points in space. The idea of time travel hasn't been just discussed in scientific circles, but has been used in many science fictions shows over the course of the genre.
As humanity spread across the universe and began to understand the cosmos better, a few began to try and develop means to travel backwards and forwards in time. The first attempt was made by launching a sublight ship from Earth towards Alpha Centauri in the year 2132. When it arrived the onboard computers registered a shorter travel time than the rest of the universe.
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 and that the radiation shields had held. 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.