  Encoded in the time- and wavelength dependent properties of pulsating AGB
stars are the underlying fundamental parameters of mass, composition and
evolutionary state. However, the standard technique of placing stars on a HR
diagram, even with the aid of pulsation periods, can not be done easily for
extended AGB stars, because of the difficulty of defining a radius or
temperature. The atmospheres of Mira variables are so extended that the optical
depth unity radius can vary by a factor of ~3 over the energetically important
region of the spectrum. Many important constituents in the radiative transfer
are far from local thermodynamic equilibrium, and for the coolest stars, the
process of dust formation and destruction requires a time-dependent model of
grain growth. I will describe the challenges and some of the solutions to
modeling these atmospheres, and describe the utility of different kinds of
observations in helping understand both fundamental parameters and chaotic
processes in complex AGB atmospheres.
