Alain Aspect, John Clauser and Anton Zeilinger have been awarded the Nobel Prize in Physics for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science. Soon after the development of the theoretical framework of quantum theory, Einstein, Podolsky, and Rosen pointed out a conceptual problem related to particles in entangled states (a purely new property which has been called as the characteristic trait of quantum mechanics by Schrödinger). Bell introduced a set of inequalities demonstrating the impossibility of predicting the outcomes of quantum measurements, without actually performing the measurement process. Experimental realizations of Bell’s predictions by Clauser’s team were followed by more precise measurements by Aspect’s group. Quantum entanglement is a new resource for recent quantum technology applications. For example, to carry a quantum state from one point to another (so-called teleportation) one needs entangled systems as shown experimentally by Zeilinger’s group. More recently, Klyachko, Can, Binicioğlu, and Shumovsky closed the gap between two dimensional quantum systems, admitting hidden variables description, and four-dimensional systems that are incompatible with such a model by constructing the so-called KCBS inequality for a three-dimensional spin-1 system. The first experimental test of the KCBS inequality has also been realized by Zeilinger’s group.