Warping space and claiming FTL makes no more sense than having a foot-race with your mate and finding a short-cut while sending him the long way around.
However, even without warping space, when you travel fast, then your perception of time is not altered while an observer in a stationary frame of reference witnesses your clocks slowing down. From your perspective. distance appears to shrink but those you leave behind appear to go into fast-forward. This has the happy consequence of theoretically leaving Earth for the stars, accelerating to near c, decelerating and arriving in a comparatively short time from YOUR point of view. But the unhappy result that if you went home again, you would probably be greeted by your great great great great great great grandchild. (Depending on how fast and far you went).
In practice, getting near the speed of light takes a ridiculous and impractical amount of energy, and an unreasonable length of time (even in *your* frame of reference as you travel) to accelerate to top speed, and again to slow down.
When you calculate how much fuel is needed to do this acceleration, it's clear that some exotic energy source is also needed otherwise you start off with a stupidly high mass of fuel.
It just ain't practical.