How far in the future is Star Trek?

Answer 1

no, Star Trek is just a fictional (make-believe) story line that introduces audience to outerspace, and other planets....basically they want you to make-believe and use your imagination
The Star Trek universe I'm sure gives one a good idea of the real universe out there. The Star Trek universe is also the kind of future we, and further generations, would like to live in. We don't really know what will happen in the future. But, we can start by being the change we want to see in the future - the microcosm affecting the macrocosm. So, YES the things in Star Trek CAN happen in the future. We must be positive that the good things in it will happen. (Picard gives a good description of that future to Lily in 'Star Trek First Contact'.)

Answer 2

The original series from the 1960s takes place from 2266 to 2269. The setting of Star Trek: The Next Generation is 2364 to 2370. The setting of Star Trek: Deep Space Nine is 2369 to 2375. The setting of Star Trek: Voyager is 2371 to 2377. The most recent Star Trek series, Enterprise, has the earliest setting, beginning around 2151.