Quantum sensing has become a mature and broad field. It is generally related
with the idea of using quantum resources to boost the performance of a number
of practical tasks, including the radar-like detection of faint objects, the
readout of information from optical memories or fragile physical systems, and
the optical resolution of extremely close point-like sources. Here we first
focus on the basic tools behind quantum sensing, discussing the most recent and
general formulations for the problems of quantum parameter estimation and
hypothesis testing. With this basic background in our hands, we then review
emerging applications of quantum sensing in the photonic regime both from a
theoretical and experimental point of view. Besides the state-of-the-art, we
also discuss open problems and potential next steps.Comment: Review in press on Nature Photonics. This is a preliminary version to
be updated after publication. Both manuscript and reference list will be
expande