  We investigate departures from LTE in the line formation of Fe for a number
of well-studied late-type stars in different evolutionary stages. A new model
of Fe atom was constructed from the most up-to-date theoretical and
experimental atomic data available so far. Non-local thermodynamic equilibrium
(NLTE) line formation calculations for Fe were performed using 1D hydrostatic
MARCS and MAFAGS-OS model atmospheres, as well as the spatial and temporal
average stratifications from full 3D hydrodynamical simulations of stellar
convection computed using the Stagger code. It is shown that the Fe I/Fe II
ionization balance can be well established with the 1D and mean 3D models under
NLTE including calibrated inelastic collisions with H I calculated from the
Drawin's (1969) formulae. Strong low-excitation Fe I lines are very sensitive
to the atmospheric structure; classical 1D models fail to provide consistent
excitation balance, particularly so for cool metal-poor stars. A better
agreement between Fe I lines spanning a range of excitation potentials is
obtained with the mean 3D models. Mean NLTE metallicities determined for the
standard stars using the 1D and mean 3D models are fully consistent. Also, the
NLTE spectroscopic effective temperatures and gravities from ionization balance
agree with that determined by other methods, e.g., infrared flux method and
parallaxes, if one of the stellar parameters is constrained independently.
