Why entanglement matters

Abstract
One century ago Erwin Schrödinger called entanglement "... the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought". However, only in the last two decades the study of quantum entanglement in many body systems (i.e. field theories) reached such a mature stage to lead to an unprecedented exchange of ideas and concepts between fields that were previously unrelated like quantum information, high-energy physics, statistical mechanics, general relativity, condensed matter and many more. In this colloquium-style tea break, I will discuss a number of examples taken from different fields in which many-body entanglement is the characteristic physical trait.