One of the most fundamental principles of post-Einsteinian physics is the idea that the speed of light is a universal constant—nothing can go faster than light because the very concept of speed, in the standard model, is contingent on the speed of light. This presents some obvious problems. If we were to travel to Tau Ceti e (the nearest potentially habitable exoplanet) at the speed of light, it would take us 12 years.
If we were to send a message to Tau Ceti e using a powerful laser beam and receive a reply using the same technology, it would still take 24 years to hear the response. If we were to develop a sufficiently powerful telescope to look at the surface of Tau Ceti e (and one may be on the way), even the image of Tau Ceti e it displays will be 12 years old. And this is just the nearest potentially habitable exoplanet. Most are much, much further away.
So the idea of colonizing other worlds on any practical timetable by traveling to those locations, or sending messages that travel to those locations, is impossible according to the standard model of physics. The only way to arrive at a destination faster than the speed of light is to skip the journey altogether by warping the space between our point of origin and our intended destination. A physicist named Miguel Alcubierre describes a hypothetical device that might do the job, though the basic principle isn't a new one—Star Trek popularized the term "warp drive," based on the physics of warping space, in the 1960s. Michio Kaku discusses warp technology with Alcubierre here:
Yesterday's announcement on gravitational waves confirms the controversial but widely-accepted hypothesis that the universe inflated "faster" than the speed of light by, in effect, warping new space outward in all directions. This means that the physics behind warp drive technology now correspond to a known natural process. What is not known is whether we can control this process—and, more importantly, whether the forces involved are too dangerous to meddle with in the first place.