Theoretical predictions of Red Giant Branch stars' effective temperatures, colors, luminosities and surface chemical abundances are a necessary tool for the astrophysical interpretation of the visible--near infrared integrated light from unresolved stellar populations, the Color-Magnitude-Diagrams of resolved stellar clusters and galaxies, and spectroscopic determinations of red giant chemical abundances. On the other hand, the comparison with empirical constraints provides a stringent test for the accuracy of present generations of red giant models. We review the current status of red giant stars' modelling, discussing in detail the still existing uncertainties affecting the model input physics (e.g., electron conduction opacity, treatment of the superadiabatic convection), and the adequacy of the physical assumptions built into the model computations. We compare theory with several observational features of the Red Giant Branch in galactic globular clusters, such as the luminosity function bump, the luminosity of the Red Giant Branch tip and the envelope chemical abundance patterns, to show the level of agreement between current stellar models and empirical data concerning the stellar luminosities, star counts, and surface chemical abundances.

71 pages, 18 figures, PASP review (in press)