The field of quantum simulations aims at gaining a deeper understanding of complex physical quantum systems that are numerically hard or intractable to solve on classical computers by using highly controllable artificial quantum systems. The foundations for this novel and interdisciplinary field were laid out by Richard Feynman’s in his visionary lectures in the 1980s held at MIT, where he already foresaw the high potential of precisely controllable physical quantum system in order to solve complex quantum physical questions. Today, the field of quantum simulations has led to diverse applications in a wide range of fields, ranging from condensed matter physics, statistical physics, quantum optics and even quantum field theory in high-energy physics. A vast range of systems are currently analyzed and implemented for this purpose, including ultracold atoms & molecules in optical lattices, ion chains, quantum dots or cavity circuits. Pioneering work in this field has been carried out by researchers both at Harvard and MPG and ongoing highly successful collaborations underline the strength of both teams in this field.