  We present and discuss the theory and phenomenology of the leading twist
theory of nuclear shadowing which is based on the combination of the
generalization of the Gribov-Glauber theory, QCD factorization theorems, and
the HERA QCD analysis of diffraction in lepton-proton deep inelastic scattering
(DIS). We apply this technique for the analysis of a wide range of hard
processes with nuclei---inclusive DIS on deuterons, medium-range and heavy
nuclei, coherent and incoherent diffractive DIS with nuclei, and hard
diffraction in proton-nucleus scattering---and make predictions for the effect
of nuclear shadowing in the corresponding sea quark and gluon parton
distributions. We also analyze the role of the leading twist nuclear shadowing
in generalized parton distributions in nuclei and in certain characteristics of
final states in nuclear DIS. We discuss the limits of applicability of the
leading twist approximation for small x scattering off nuclei and the onset of
the black disk regime and methods of detecting it. It will be possible to check
many of our predictions in the near future in the studies of the
ultraperipheral collisions at the Large Hadron Collider (LHC). Further checks
will be possible in pA collisions at the LHC and forward hadron production at
the Relativistic Heavy Ion Collider (RHIC). Detailed tests will be possible at
an Electron-Ion Collider (EIC) in the USA and at the Large Hadron-Electron
Collider (LHeC) at CERN.
