Photon-by-photon quantum light state engineering

The ability to manipulate light at the level of single photons, its elementary excitation quanta, has recently made it possible to produce a rich variety of tailor-made quantum states and arbitrary quantum operations, of high interest for fundamental science and applications. Here we present a concise review of the progress made over the last few decades in the engineering of quantum light states. Although far from exhaustive, this review aims at providing a sufficiently wide and updated introduction that may serve as the entry point to such a fascinating and rapidly evolving field.