In 2012, two mathematicians published a paper in a British scientific journal, claiming that there's a way to crunch Einstein's calculations and show that faster-than-light velocities are indeed possible.
But if those dissenters turn out to be right, we'd still have to actually find some proof that particles can move faster than light speed, and so far we haven't.
There was one highly-publicized 2011 experiment, in which researchers at the CERN particle accelerator in Europe supposedly clocked particles called neutrinos moving an extremely tiny bit faster than Einstein's speed limit.
But as it turned out, a glitch in the fiber-optic cable in the researchers' equipment apparently caused a false reading.