  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.
