Headwind: Modelling Mass Loss of AGB Stars, Against All Odds

The intricate interplay of atmospheric shock waves and a complex, variable radiation field with non-equilibrium dust formation presents a considerable challenge to self-consistent modelling of atmospheres and winds of AGB stars. Nevertheless it is clear that realistic models predicting mass loss rates and synthetic spectra are crucial for our understanding of this important phase of stellar evolution. While a number of questions are still open, significant progress has been achieved in recent years. In particular, self-consistent models for atmospheres and winds of C-stars have reached a level of sophistication which allows direct quantitative comparison with observations. In the case of stars with C/O < 1, however, recent work points to serious problems with the dust-driven wind scenario. This contribution analyzes the basic ingredients of this scenario with analytical estimates, focusing on dust formation, non-grey effects, and differences between C-rich and O-rich environments, as well as discussing the status of detailed dynamical wind models and current trends in this field.