We review the nuclear parton distribution functions computed on the basis of our microscopic model taking into account a number of nuclear effects including Fermi motion and nuclear binding, nuclear meson-exchange currents, off-shell corrections to bound nucleon distributions and nuclear shadowing. We discuss applications to a number of different processes including lepton-nucleus deep inelastic scattering, proton-nucleus Drell-Yan lepton pair production at Fermilab, as well as $W^\pm$ and $Z^0$ boson production in proton-lead collisions at the LHC.