  Cool giant stars are highly dynamical objects, and complex micro-physical
processes play an important role in their extended atmospheres and winds. The
interpretation of observations, and in particular of high-resolution IR
spectra, requires realistic self-consistent model atmospheres. Current
dynamical models include rather detailed micro-physics, and the resulting
synthetic spectra compare reasonably well with observations. A transition from
qualitative to quantitative modelling is taking place at present. We give an
overview of existing dynamical model atmospheres for AGB stars, discussing
recent advances and current trends in modelling, including 3D 'star-in-a-box'
models. When comparing synthetic spectra and other observable properties
resulting from dynamical models with observations we focus on the near- and
mid-IR wavelength range.
