The first steps towards interstellar travel have been taken, but the stars are very far away. Voyager 1 is about 17 light-hours distant from Earth and is traveling with a velocity of 0.006 percent of light speed, meaning it will take about 17,000 years to travel one light-year. Fortunately, the elusive "warp drive" now appears to be evolving past difficulties with new theoretical advances and a NASA test rig under development to measure artificially generated warping of space-time.
The warp drive broke away from being a wholly fictional concept in 1994, when physicist Miguel Alcubierre suggested that faster-than-light (FTL) travel was possible if you remained still on a flat piece of spacetime inside a warp bubble that was made to move at superluminal velocity. Rather like a magic carpet.