  In this review, we present the current status of phenomenological research on
constraining the multi-dimensional proton (and nucleus) structure at high
energies through studies of the so-called gluon Wigner distributions. We
provide a brief pedagogical introduction into the corresponding theoretical
definitions and modelling of exclusive and diffractive scattering observables
in terms of the Wigner distribution. Also, we present a detailed outlook into
the existing and planned experimental measurements that attempt to constrain
the Wigner distribution. We briefly overview possible interconnections between
various manifestations of the gluon Wigner distribution emerging, for instance,
in azimuthal-angle correlations in (semi)exclusive reactions and elliptic flow
measurements in inclusive processes. We also summarise the current knowledge on
the most important processes that would potentially enable one to constrain the
elliptic gluon density in the proton and to separate it from the genuine effect
of hydrodynamic evolution in the flow measurements.
