A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging

•Description of the state-of-the-art of the theoretical tools for multiparameter quantum estimation.•Perspective on theoretical and fundamental open questions in multiparameter quantum estimation.•Description of state-of-the-art in (multiparameter) quantum imaging: from superresolution to phase-imaging.•Perspective on future applications of multiparameter quantum estimation. The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such multiparameter estimation can be achieved depends on understanding the many subtleties that come into play: establishing solid foundations is key to delivering future technology for this task. In this article we discuss the state of the art of quantum multiparameter estimation, with a particular emphasis on its theoretical tools, on application to imaging problems, and on the possible avenues towards the next developments.