Theoretical models of asymptotic giant branch stars

Low and intermediate-mass stars are the most numerous evolved stars in galaxies, and are important chemical factories when on the asymptotic giant branch (AGB). AGB stars that experience He-shell instabilities - or thermal pulses - are known as thermally-pulsing AGB stars and are observed as cool, bright giants and supergiants. Thermal pulses drive mixing between the core and envelope, while episodic mass-loss erodes the envelope, enriching the interstellar medium.  AGB stars are also long period variables, covering a range of variability types from semi-regular to Mira, with periods typically on the order of a 100 days or more, with the longest period AGB stars observed with periods of up to 2,000 days. The variability of an AGB stars has been intrinsically linked with mass-loss.
In this talk, I review theoretical stellar models of AGB stars, highlighting where progress has been made in recent years and discuss areas that are still in need of improvement. I will also highlight where studies of pulsations of AGB stars coupled with theory have improved our understanding of the structure and evolution of these complex objects.