  Determining the inner structure of protons and nuclei in terms of their
fundamental constituents has been one of the main tasks of high energy nuclear
and particle physics experiments. This quest started as a mapping of the
(average) parton densities as a function of longitudinal momentum fraction and
resolution scale. Recently, the field has progressed to more differential
imaging, where one important development is the description of the
event-by-event quantum fluctuations in the wave function of the colliding
hadron.
  In this Review, recent developments on the extraction of proton and nuclear
transverse geometry with event-by-event fluctuations from collider experiments
at high energy is presented. The importance of this fundamentally interesting
physics in other collider experiments like in studies of the properties of the
Quark Gluon Plasma is also illustrated.
