  The bad metal behavior in the normal state of the iron-based superconductors
suggests an intimate connection between the superconductivity and a proximity
to a Mott transition. At the same time, there is strong evidence for the
multi-orbital nature of the electronic excitations. It is then important to
understand the orbital-dependent effects of electron correlations. In this
paper we review the recent theoretical progresses on the metal-to-insulator
transition in multiorbital models for the iron-based superconductors. These
include studies of models that contain at least the 3d xy and 3d xz/yz models,
using a slave-spin technique. For commensurate filling corresponding to that of
the parent iron pnictides and chalcogenideds, a Mott transition generally
exists in all these models. Near the Mott transition, a strongly correlated
metal exhibiting bad metal features and strong orbital selectivity is
stabilized due to the interplay of Hund's coupling and orbital-degeneracy
breaking. Particularly for the alkaline iron selenides, the ordered vacancies
effectively reduce the kinetic energy, thereby pushing the system further into
the Mott-insulating regime; in the metallic state, there exists an
orbital-selective Mott phase in which the iron 3d xy orbital is Mott localized
while the other 3d orbitals are still itinerant. An overall phase diagram for
the alkaline iron selenides has been proposed, in which the orbital-selective
Mott phase connects between the superconducting phase and the Mott-insulating
parent state.
