I will present a recent theorem that asserts that there cannot exist an "extension of quantum theory" that allows us to make more informative predictions about future measurable events (e.g., whether a horizontally polarized photon passes a polarization filter with a given orientation) than standard quantum theory. The theorem is based on two assumptions about the extended theory: (i) the theory should be compatible with quantum theory (this means, in practice, that the theory is not falsified by current experimental data); (ii) the theory should not preclude experimenters from freely choosing the measurement settings. More precisely, the latter assumption corresponds to the requirement that measurement settings can be chosen at random such that they are independent of any other events, except of course those that lie in the causal future of the choice (i.e., in its future light cone). In addition, I will discuss a corollary of the non-extendibility theorem which leads to the same conclusions as a recent theorem by Pusey, Barrett, and Rudolph on the "reality of the quantum state", based only on the above assumptions.