Wormholes, those notoriously unstable warps in space and time, could theoretically be kept stable long enough for a beam of light to be sent through them. Exiting at the far end, these beams of light could find themselves anywhere in the universe, and theoretically, time as well. If the beam of light were used to carry a message, humanity could actually find itself with the capability of communicating across the ages.
That's the theory at least, put forth by University of Cambridge research fellow Luke Butcher. By generating something called Casimir energy, which creates a sort of low-pressure zone in space-time, Butcher believes that we could slow the degradation of naturally-occurring wormholes. The wormholes would still wink out of existence fairly quickly, so you can forget piloting your Intrepid-class Voyager spaceship through it to the Delta Quadrant.
Even getting a message-carrying pulse of light through a wormhole would require the right conditions. The wormhole itself would have to be massively longer than its mouth is wide to be capable of generating the Casimir energy needed to keep it stable long enough to fire a message through it. If we do find that all this is possible, there's a very small chance that we not only find a perfectly shaped wormhole, but also someone on its other end watching.
To really make use of a faster-than-light communications device, we'd have to figure out how to manufacture wormholes ourselves. Sadly, for now, that technology remains firmly planted in the realms of sci-fi.