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Towards the end of 2011, Pusey, Barrett and Rudolph derived a theorem thataimed to show that the quantum state must be ontic (a state of reality) in abroad class of realist approaches to quantum theory. This result attracted alot of attention and controversy. The aim of this review article is to reviewthe background to the Pusey--Barrett--Rudolph Theorem, to provide a clearpresentation of the theorem itself, and to review related work that hasappeared since the publication of the Pusey--Barrett--Rudolph paper. Inparticular, this review: Explains what it means for the quantum state to beontic or epistemic (a state of knowledge); Reviews arguments for and against anontic interpretation of the quantum state as they existed prior to thePusey--Barrett--Rudolph Theorem; Explains why proving the reality of thequantum state is a very strong constraint on realist theories in that it wouldimply many of the known no-go theorems, such as Bell's Theorem and the need foran exponentially large ontic state space; Provides a comprehensive presentationof the Pusey--Barrett--Rudolph Theorem itself, along with subsequentimprovements and criticisms of its assumptions; Reviews two other arguments forthe reality of the quantum state: the first due to Hardy and the second due toColbeck and Renner, and explains why their assumptions are less compelling thanthose of the Pusey--Barrett--Rudolph Theorem; Reviews subsequent work aimed atruling out stronger notions of what it means for the quantum state to beepistemic and points out open questions in this area. The overall aim is notonly to provide the background needed for the novice in this area to understandthe current status, but also to discuss often overlooked subtleties that shouldbe of interest to the experts.

Is the quantum state real? An extended review of $\psi$-ontology theorems