The future was the set of all events that occurred after a given point in time, following one's present, which was itself preceded by the past. In regards to time travellers, the concept of past, present and future was relative.
For her first trip in the Doctor's TARDIS, Rose Tyler, a native of the year 2005, asked to go forwards in time when given the option by the Ninth Doctor. Advancing through the Time Vortex, the TARDIS landed in 2105 then 12005, though the Doctor and Rose only stepped out of the TARDIS when it arrived in the year 5,000,000,000. (TV: The End of the World)
Despite initially accepting that he would take Martha Jones on "just one trip" in the TARDIS, the Tenth Doctor "stretch[ed] the definition" to allow for a trip to her relative past as well as a trip to her relative future. (TV: Gridlock)
As a result of Jack Harkness jumping on to it as it departed Cardiff in 2008, the TARDIS accelerated into the future, through 1,000,000,000, 5,000,000,000, 5,000,000,000,000, 50,000,000,000 before finally landing on Malcassairo in the year 100,000,000,000, the end of the universe. (TV: Utopia)
In River Song's World, Charles Dickens promoted his "new Christmas special" on television as involving ghosts and the past, the present and future, all at the same time. (TV: The Wedding of River Song)
While attempting to flee from the sentient oil with Nardole and Bill Potts, the Twelfth Doctor took the TARDIS 23 million years into the future from the perspective of Bill, a native of the year 2017. (TV: The Pilot) For her first trip in the TARDIS following this ordeal, Bill asked to go to the future when given the option. When asked why, Bill explained that she wanted to see if the future was happy. (TV: Smile)