  We review the theoretical and experimental progress in the Glauber model of
multiple nucleon and/or parton scatterings, after the last 10--15 years of
operation with proton and nuclear beams at the CERN Large Hadron Collider (LHC)
and with various light and heavy colliding ions at the BNL Relativistic Heavy
Ion Collider (RHIC). The main developments and the state-of-the-art of the
field are summarized. These encompass measurements of the inclusive inelastic
proton and nuclear cross sections, advances in the description of the proton
and nuclear density profiles and their fluctuations, inclusion of subnucleonic
degrees of freedom, experimental procedures and issues related to the
determination of the collision centrality, validation of the binary scaling
prescription for hard scattering cross sections, and constraints on transport
properties of quark-gluon matter from varying initial-state conditions in
relativistic hydrodynamics calculations. These advances confirm the validity
and usefulness of the Glauber formalism for quantitative studies of QCD matter
produced in high-energy collisions of systems, from protons to uranium nuclei,
of vastly different size.
