Core helium burning and low-metallicity AGB stars: structure and evolution ConstantinoThomas 2017 In this thesis we scrutinize and improve theoretical models of the two helium burning stages of low-mass (less than about 8 solar masses) stellar evolution – the core helium burning (CHeB) and asymptotic giant branch (AGB) phases. Accurate stellar models of these phases are essential for the understanding of the physics of stars, the chemical evolution of galaxies, and astrophysics more generally, where the observation of starlight is paramount. In this study we use new models and observational data to investigate two particular important uncertainties during the CHeB and AGB stages that have compounding effects on the evolution. In CHeB models, feedback from convective overshoot can lead to the development of a ‘semiconvection’ zone outside the convective core that can extend the lifetime of the phase by up to a factor of two. In the later thermally pulsing-AGB phase, accounting for the opacity increase due to in situ composition changes can increase the stellar radius, and therefore mass loss rate, truncating the evolution. We compute a grid of CHeB stellar models with four different treatments of convective boundaries using the Monash University stellar evolution code MONSTAR. Theoretical non-radial adiabatic pulsations for these models are then compared with recent asteroseismic observations from the Kepler telescope. Next, we infer the horizontal branch and AGB lifetimes of globular cluster stars from star counts in HST photometry and compare these with predictions from evolution sequences with the different mixing schemes. Finally, for models of the thermally-pulsing AGB phase we incorporate into MONSTAR new low-temperature molecular opacity data that accounts for changes in the surface abundance of carbon, nitrogen, and oxygen. The effect of this update is tested by computing a grid of low-metallicity AGB models that experience the third dredge-up. We identify two distinct CHeB structures that can simultaneously match the globular cluster and asteroseismic observations: those with (i) a slowly mixing region outside the convective core that traps oscillation modes, or (ii) the largest possible convective core, requiring a novel scheme for convective overshoot. We may be able to discriminate between these two possibilities with further work, including the analysis of biases in the observed sample and multi-dimensional simulations. The inclusion of composition-dependent low-T opacity in low-metallicity models shortens the AGB lifetime, increases the mass threshold for hot bottom burning, and radically affects chemical yields. By computing initially metal-free models, we demonstrate that if the third dredge-up occurs, there is no metallicity below which composition-dependent low-T opacity may be neglected. The reduced nitrogen yield from models with the new opacity may help explain the observed numbers of carbon- and nitrogen-enhanced metal-poor stars: this should be confirmed with binary population synthesis calculations.