Well, the most well-known one is Warp speed, that's what Star Trek uses to describe faster-than-light speed.
Warp 1 is light speed, and warp 2, warp 3, warp 8, etc... well, that's faster.
In Star Wars, they talk about jumping into "hyperspace". We don't know much about it other than it makes stars look like trippy lines through the window, and that it can take you to the other side of the galaxy fairly quickly.
In Babylon 5, "hyperspace" is a sort of parallel universe that spaceships can jump into, with the help of specially designed gates that create interdimensional holes, and a short trip in hyperspace (which is sort of like space, but much more red, and no planets) corresponds to a long trip in "real" space.
In Battlestar Galactica (the 21st century version), capital ships have a jump drive that can make a "jump" that basically teleports them to another star system. They don't explain it any more than that.
In Doctor Who, the Doctor's time machine, the Tardis, enters the Time Vortex and from there it can reach anywhere in time and space. So I suppose that's another example of using a "sub-reality" that bypasses the physics of our universe.
So, those are the big FTL concepts that have already been used. If you are writing science fiction, you could come up with something similar and possibly get away with it, or you could invent an entirely new way to describe faster-than-light travel. If you're doing science fiction, you will want to have some seriously cool imagination.