Relativity actually says that all things with a real mass must go slower than the speed of light, all things with zero mass must go at the speed of light, and all things with imaginary mass must go faster than the speed of light. Your guess is as good as mine on how to get things with imaginary mass, though.
Well, it is just basic 23rd century physics...tachyons (which would actually be a cool name for a band, if the lead singer was bald and had a cool British accent). If you insist on crude 21st century science, then tachyons are a largely defunct theoretical construct, though I do believe some variants of string theory suggest they exist.