 In the May 15, 1935 issue of Physical Review Albert Einstein co-authored a paper with his two postdoctoral research associates at the Institute for Advanced Study, Boris Podolsky and Nathan Rosen. The article was entitled “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?” (Einstein et al. 1935). Generally referred to as “EPR”, this paper quickly became a centerpiece in debates over the interpretation of quantum theory, debates that continue today. Ranked by impact, EPR is among the top ten of all papers ever published in Physical Review journals. Due to its role in the development of quantum information theory, it is also near the top in their list of currently “hot“ papers. The paper features a striking case where two quantum systems interact in such a way as to link both their spatial coordinates in a certain direction and also their linear momenta (in the same direction), even when the systems are widely separated in space. As a result of this “entanglement”, determining either position or momentum for one system would fix (respectively) the position or the momentum of the other. EPR prove a general lemma connecting such strict correlations between spatially separated systems to the possession of definite values. On that basis they argue that one cannot maintain both an intuitive condition of local action and the completeness of the quantum description by means of the wave function. This entry describes the lemma and argument of that 1935 paper, considers several different versions and reactions, and explores the ongoing significance of the issues raised.