Quantum foundations is a discipline of science that seeks to understand the most counter-intuitive aspects of quantum theory, reformulate it and even propose new generalizations thereof. Contrary to other physical theories, such as general relativity, the defining axioms of quantum theory are quite ad hoc, with no obvious physical intuition. While they lead to the right experimental predictions, they do not come with a mental picture of the world where they fit.

There exist different approaches to resolve this conceptual gap:

Research in quantum foundations is structured along these roads.

Two or more separate parties conducting measurements over a quantum state can observe correlations which cannot be explained with any local hidden variable theory. Whether this should be regarded as proving that the physical world itself is "nonlocal" is a topic of debate, but the terminology of "quantum nonlocality" is commonplace. Nonlocality research efforts in quantum foundations focus on determining the exact limits that classical or quantum physics enforces on the correlations observed in a Bell experiment or more complex causal scenarios. This research program has so far provided a generalization of Bell's theorem that allows falsifying all classical theories with a superluminal, yet finite, hidden influence.

Nonlocality can be understood as an instance of quantum contextuality. A situation is contextual when the value of an observable depends on the context in which it is measured (namely, on which other observables are being measured as well). The original definition of measurement contextuality can be extended to state preparations and even general physical transformations.

A physical property is epistemic when it represents our knowledge or beliefs on the value of a second, more fundamental feature. The probability of an event to occur is an example of an epistemic property. In contrast, a non-epistemic or ontic variable captures the notion of a "real" property of the system under consideration.

There is an on-going debate on whether the wave-function represents the epistemic state of a yet to be discovered ontic variable or, on the contrary, it is a fundamental entity. Under some physical assumptions, the Pusey–Barrett–Rudolph (PBR) theorem demonstrates the inconsistency of quantum states as epistemic states, in the sense above. Note that, in QBism and Copenhagen-type views, quantum states are still regarded as epistemic, not with respect to some ontic variable, but to one's expectations about future experimental outcomes. The PBR theorem does not exclude such epistemic views on quantum states.

Some of the counter-intuitive aspects of quantum theory, as well as the difficulty to extend it, follow from the fact that its defining axioms lack a physical motivation. An active area of research in quantum foundations is therefore to find alternative formulations of quantum theory which rely on physically compelling principles. Those efforts come in two flavors, depending on the desired level of description of the theory: the so-called Generalized Probabilistic Theories approach and the Black boxes approach.