In 1935 Einstein, Podolsky, Rosen (EPR) and (independently) Schrödinger realized that the probabilistic nature of quantum mechanics predicted the existence of a strange phenomenon: two particles can be linked together such that the properties of one particle cannot be described independently of the other, even if they are separated by an infinite distance. This is the so-called entanglement.
Their goal was to "attack" quantum theory by showing the incompatibility of entanglement with the principles of locality and realism that had been the cornerstone of physics up to that time; however, they ended up introducing one of the most fundamental aspects of quantum mechanics.
After 1964, when John Bell mathematically rephrased the EPR's arguments by deriving his famous inequality, various experiments have been able to test this "spooky action at distance" (as Einstein used to refer to it). Moreover entanglement has turned out to be an important resource for both fundamental and practical reasons.

The research for my PhD is focused on the theory of entanglement: the main goal is to study and characterize entanglement in different types of systems and theoretical models to see if this striking property of quantum mechanics can give insights into fundamental questions.