So the recent maybe-discovery by CERN of some possibly-faster-than-light neutrinos has been garnering a lot of attention lately. Predictably, people are claiming that this result, if true, destroys everything we thought we knew about physics. For people convinced by this argument, please see my previous post.
Because the Theory of Relativity posits a constant speed of light as the upper bound to velocity in the universe, this result (if true) invalidates the Theory, and with it much of modern physics. Or so the theory goes. While it is true that we'd have to scrap the Theory of Relativity in its current form, it is by no means the case that this would have any meaningful impact on, well, anything. It really just comes down to the "things with big effects have big evidence" principle. If anything about the Theory of Relativity was really really wrong we'd have noticed by now, on account of all of our predictions using it being really really wrong. As they haven't been, we know that this result (if true) will require at most minor modifications to the theory.
Maybe neutrinos are the speed limit bearing particles now? Maybe we need to add another term to an equation or two. Or maybe we just need to add in a "neutrinos under certain circumstances" exception to the model.
Science is about building models that make true predictions. Any model is useful exactly to the degree to which it aids us in making true predictions. Relativity is almost preternaturally useful by this metric, and will not be scrapped on account of one inconsistency. Incidentally, this is also true of things like evolution, gravity, and conceptions of a spherical earth. Problems will come up (like, for instance, we have no idea what actually allows particles to have gravitational interactions... and the earth is actually a little bit fat in the middle with all sorts of weird bumps and protuberances), but so long as they don't interfere too terribly with the predictive power of the theories (stuff falls, and great circle paths are faster than "straight" ones) we keep them around. Welcome to Science, and more broadly, Thinking.