The mainstream thought is that they are real and undetected, but there are theories that they aren't and there's plenty of attempts to modify laws to explain them away (and I suspect there's some wistful thinking that there's maybe a Noble prize there, so there's already been a fair bit of work done, even though it's very controversial).
To be fair, the last time someone explored a discrepancy between known physics and empirical observation we got quantum mechanics and relativity. There is a commonly held belief that as observations outpace theory that we'll have a similar leap in technology. I think this is why everyone was so excited about the LHC and Kepler Observatory.
I don't know whether the next breakthrough in physics will be quite as relevant in our lives as quantum and relativistic physics. It would be nice if we could link gravity and E/M like we did with the strong and weak forces. Who knows what we could do if we knew how those two go together.
