  Recent work has revealed the central role played by the Kirkwood-Dirac
quasiprobability (KDQ) as a tool to properly account for non-classical features
in the context of condensed matter physics (scrambling, dynamical phase
transitions) metrology (standard and post-selected), thermodynamics (power
output and fluctuation theorems), foundations (contextuality, anomalous weak
values) and more. Given the growing relevance of the KDQ across the quantum
sciences, our aim is two-fold: First, we highlight the role played by
quasiprobabilities in characterizing the statistics of quantum observables and
processes in the presence of measurement incompatibility. In this way, we show
how the KDQ naturally underpins and unifies quantum correlators, quantum
currents, Loschmidt echoes, and weak values. Second, we provide novel
theoretical and experimental perspectives by discussing a wide variety of
schemes to access the KDQ and its non-classicality features.
