Late-type giants (RGB/AGB stars) will be important tracers of the Galactic morphology and evolution in the framework of Gaia, as they are intrinsically bright and thus can probe distant stellar populations or those obscured by interstellar extinction. A realistic representation of their atmospheres and spectra with stellar atmosphere models is thus of crucial importance, both for the design and optimization of Gaia instruments, as well as the interpretation of provided astrophysical data. Our analysis of synthetic photometric colours of late-type giants based on PHOENIX, MARCS and ATLAS model atmospheres indicates a general agreement between the current theoretical predictions and observations in the framework of stationary I-D model atmospheres. Presently available models allow temperature determinations of RGB/AGB stars to an accuracy of similar to +/- 100 K. In an exploratory study we try to quantify possible residual systematic effects due to the approximations made in 1-D models using full 3-D hydrodynamical models. We find that differences in broad-band photometric colours calculated with I-D and 3-D models are significant, translating to the offsets in effective temperature of up to Delta T-eff similar to 70 K. Clearly, full 3-D hydrodynamical models will help to alleviate such ambiguities in current theoretical modelling. Additionally, they will allow to study new phenomena, to open qualitatively new windows for stellar astrophysics in the Gaia-era.