We show that contrary to what is expected from 1D stationary model atmospheres, 3D hydrodynamical modeling predicts a considerable influence of convection on the spectral properties of late-type giants. This is due to the fact that convection overshoots into the formally stable outer atmospheric layers producing a notable granulation pattern in the 3D hydrodynamical models, which has a direct influence on the observable spectra and colors. Within the framework of standard 1D model atmospheres the average thermal stratification of the 3D hydro model can not be reproduced with any reasonable choice of the mixing length parameter and formulation of the turbulent pressure. The differences in individual photometric colors – in terms of 3D versus 1D – reach up to $\sim0.2$ mag, or $\Delta T_{\rm eff}\sim70$ K. We discuss the impact of full 3D hydrodynamical models on the interpretation of observable properties of late-type giants, briefly mentioning problems and challenges which need to be solved for bringing these models to a routine use within the astronomical community in 5–10 years from now.