This can be anything from Hyperspace in Star Wars, Warp Drive in Star Trek, travel through the Warp in Warhammer 40k or anything else.
I’ve always liked “slow” FTL travel, where going a few light-years still takes a few days or so. I also really like travel through an alternate dimension like in 40k, Event Horizon, Witchspace in Elite Dangerous.
I wanna know your favorite versions, or do you prefer stories that obey the laws of known physics, like the Expanse or Rimworld?
I prefer the STL in Card’s Ender’s Game series. They asymptotically approach the speed of light so the passengers only have several weeks pass when travelling to far flung locations but the universe around them experiences a normal passage of time which may be tens of years. This has really big implications on the plots in several stories.
They do have an ansible communications system that does allow instantaneous communication over astronomical distances.