I present here the main results of recent realistic, 3D, hydrodynamical simulations of convection at the surface of metal-poor red giant stars. I discuss the application of these convection simulations as time-dependent, 3D, hydrodynamical model atmospheres to spectral line formation calculations and abundance analyses. The impact of 3D models on derived elemental abundances is investigated by means of a differential comparison of the line strengths predicted in 3D under the assumption of local

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... thermodynamic equilibrium (LTE) with the results of analogous line formation calculations performed with classical, 1D, hydrostatic model atmospheres. The low surface temperatures encountered in the upper photospheric layers of 3D model atmospheres of very metal-poor stars cause spectral lines of neutral metals and molecules to appear stronger in 3D than in 1D calculations. Hence, 3D elemental abundances derived from such lines are significantly lower than estimated by analyses with 1D models. In particular, differential 3D-1D LTE abundances for C, N, and O derived from CH, NH, and OH lines are found to be in the range -0.5 to -1 dex. Large negative differential 3D-1D corrections to the Fe abundance are also computed for weak low-excitation neutral Fe lines. The application of metal-poor 3D models to the spectroscopic analysis of extremely iron-poor halo stars is discussed.