Late-type giants (i.e., stars on the red and asymptotic giant branches, RGB/AGB, respectively) are dominant contributors to the overall spectral appearance of intermediate age and old stellar populations, especially in the red/near-infrared part of the spectrum. Being intrinsically bright, they are well suited for probing distant/obscured populations, especially those that can not be studied with their fainter members, like main sequence turn-off stars or subgiants. Late-type giants and supergiants will be the only stellar types accessible in intermediate age and old populations beyond the distances of several Mpc with the future 30-50 m class extremely large telescopes (Olsen et al. 2003). Indeed, proper understanding of their observable properties by means of theoretical models is of key importance for studying the evolution of stellar populations and their host galaxies.