  The winds observed around asymptotic giant branch (AGB) stars are generally
attributed to radiation pressure on dust, which is formed in the extended
dynamical atmospheres of these pulsating, strongly convective stars. Current
radiation-hydrodynamical models can explain many of the observed features, and
they are on the brink of delivering a predictive theory of mass loss. This
review summarizes recent results and ongoing work on winds of AGB stars,
discussing critical ingredients of the driving mechanism, and first results of
global 3D RHD star-and-wind-in-a-box simulations. With such models it becomes
possible to follow the flow of matter, in full 3D geometry, all the way from
the turbulent, pulsating interior of an AGB star, through its atmosphere and
dust formation zone into the region where the wind is accelerated by radiation
pressure on dust. Advanced instruments, which can resolve the stellar
atmospheres, where the winds originate, provide essential data for testing the
models.
