  We review theoretical investigations on the origin of the orbital selective
phase where localized and itinerant electrons coexist in the d shell at
intermediate strength of the on-site Coulomb interactions between electrons. In
particular, the effect of spatial fluctuations on the phase diagram of the
two-orbital Hubbard model with unequal bandwidths is discussed. And different
band dispersions in different orbitals as well as different magnetically
ordered states in different orbitals which are responsible for orbital
selective phase transitions are emphasized. This is due to the fact that these
two mechanisms are independent of the Hund's rule coupling, and are completely
distinct from other well-known mechanisms like orbitals of unequal bandwidths
and orbitals with different degeneracies. Moreover, crystal field splitting is
not required in these two recently proposed mechanisms.
