  QM has the peculiar property that quantum-mechanical states imply, in general, only statistical restrictions on the results of measurements.  The natural conclusion to be drawn is that these states are incomplete descriptions of quantum systems. QM, thus, would be incomplete in the sense that a typical QM state description of an individual system could be supplemented with a more complete description in terms of an HV theory. In an HV description of the system the QM probabilities would be naturally interpreted as epistemic probabilities of the sort that arise in ordinary statistical mechanics. Such an HV description might not be practically useful, but one is tempted to think that it should at least be possible in principle. There are, however, two powerful theorems to the effect that such a description is subject to severe  constraints: QM, given certain at least prima facie plausible premises,  cannot be supplemented by an HV theory. The more famous of these two  theorems is Bell’s theorem which states that, given a premise of locality, an HV model cannot match the statistical predictions of QM. The second important no-go theorem against HV theories is the theorem of Kochen and Specker (KS) which states that, given a premise of noncontextuality (to be explained presently) certain sets of QM observables cannot consistently be assigned values at all (even before the question of their statistical distributions arises).