All good comments above but @Dibs seems a little hazy about what constitutes the standard model and the regions of validity of its components. Without getting into too much technical detail, here is my attempt to clarify the situation.
QCD is the theory of the strong interaction. It is unusual among physical theories in that it seems to work better for high energy processes than low energy processes. What I mean by "work better" is that it is easier to perform the computations and compare the results with experiments. For low energy interactions between hadrons, for example, we cannot calculate with precision the interaction between two nucleons and so we are forced to employ effective meson exchange models if we wish to study nuclei. It is far from a theory that "describes it all in perfect detail."
QED (the quantum theory of the electromagnetic interaction) is the closest we come to a "really complete and completely valid" theory. It can be used to calculate certain quantities to ten significant digits (which matches the current limits of experiment). This theory could be pushed further should experimental improvements justify the effort.
QED has been unified with the weak nuclear interaction (the theory of beta decay) to form the electro-weak theory and this has been unified with QCD to form what we call the standard model. The standard model is not complete, however, because it does not incorporate gravity and, furthermore, has no explanation for dark matter, or for the big bang itself. Some might also include dark energy in the list of excluded phenomenon, but see my answer to this question: Are there experiments taking place right now that might show evidence for or falsify dark energy or dark matter? for a possible explanation for dark energy that falls within the standard model.
A final comment: The basic difference between physics and mathematics is the level of precision that is attainable. We can know with certainty the value of pi to millions of significant digits but the best that can be done with physics will always pale in comparison.