  During the recent years significant progress has been made in the modeling of
red giant atmospheres with the aid of 3D hydrodynamical model atmosphere codes.
In this contribution we provide an overview of selected results obtained in
this context by utilizing 3D hydrodynamical CO5BOLD stellar model atmospheres.
Hydrodynamical simulations show that convective motions lead to significant
differences in the atmospheric structures of red giants with respect to those
predicted by the classical 1D model atmospheres. Results of these simulations
also show that in certain cases 1D models fail to reproduce even the average
properties of the 3D hydrodynamical models, such as P-T profiles. Large
horizontal temperature fluctuations in the 3D model atmospheres, as well as
differences between the temperature profiles of the average <3D> and 1D models,
lead to large discrepancies in the strengths of spectral lines predicted by the
3D and 1D model atmospheres. This is especially important in models at lowest
metallicities ([M/H]<-2.0) where the 3D-1D abundance differences may reach (or
even exceed) -0.6 dex for lines of neutral atoms and molecules. We also discuss
several simplifications and numerical aspects involved in the present 3D
hydrodynamical modeling of red giant atmospheres, and briefly address several
issues where urgent progress may be needed.
