There is a lot that we know in fundamental physics - which is to say the scientific endeavor of determining the most basic sets of laws of physics from which all other scientific phenomena can be derived, at least in principal, if not in practice. Most of that is captures in two basic theoretical constructs: Einstein's law of general relativity, and the Standard Model. General relativity has emerged remarkably in tact after about a century. The Standard Model has undergone some minor renovations over the last half century, most recently imparting mass to neutrinos, but has also been remarkably robust in the face of precision tests.
For all of that, most physicists do not believe that we have learned all that there is to learn, and that there are theories of fundamental physics yet to be discovered.
General relativity and the Standard Model are not perfectly compatible at a theoretical level, even though their inconsistencies generally arise in unobservable contexts. There is not yet a widely accepted and empirically supported theory of quantum gravity.
We have equations for quantum chromodynamics (strong force interactions between quarks), but are still somewhat fuzzy about what those equations imply. Numerical models based upon these equations currently surpass our ability to confirm their predictions experimentally and there is not complete consensus regarding how to go about making numerical predictions from these equations (which are too hard mathematically to computer exactly and directly from the equations).
Our theories regarding dark matter and dark energy phenomena are still works in progress.
The weak force shows greater charge-parity violations than we would expect, while the strong force shows none experimentally despite equation terms that could naturally provide for them.
We observe differences in properties between muonic hydrogen spectrums and ordinary hydrogen spectrums, but it isn't really clear why these occur.
One Standard Model particle, the Higgs boson (there may be more than one kind of them), has not yet been discovered (although a definitive determination regarding its existence is very likely within the next couple of years).
We haven't definitely ruled out a whole menagerie of theoretically proposed particles, and if dark matter is a result of some kind of matter not yet directly observed we need at least one more than we've observed to make the laws of the universe complete.
Efforts to come up with any more profound reason for the many constants in the Standard Model are so far without a clear winner.
With the large hadron collider, and a number of lower profile fundamental physics experiments, up and running, we are receiving an immense amount of new data. But, we have failed to see anything that strongly favors extensions of the Standard Model such as supersymmetry, string theory, technicolor, preon theories, or loop quantum gravity. Neutrino experiments are hinting that there may be more than three flavors of neutrinos. There are perhaps half a dozen unexplained results from high energy physics experiments, but none definitive or well understood theoretically.
False alarms seem to be common, mostly because error estimates in physics experiments ignore "unknown unknowns" that turn out to be pretty important sometimes.
While it seems more and more clear that somewhere in all the smoke of phenomena that don't quite match theoretical expectations there must be fire, the constraints on any extensions of the Standard Model or General Relativity are tightening each year with new results. We don't have the exact laws of the universe on the books, but we are close. The Standard Model needs tweaking, but not much, even in highly eosteric circumstances. General Relativity is at least a very good classical approximation of how the universe behaves. The flaws in these theories are in domains that are hard to measure and hence don't necessarily have much practical application.
My own intuition is that we will find less, rather than more, in the next few years. Far more theories for extensions of the Standard Model will be ruled out than established. The possibility that we will empirically rule out all Standard Model Higgs boson possibilities is real. The possibility that we will still see no supersymmetric particles or phenomena is great.