Simulations of stellar convection The surface layers of cool stars, including the Sun, are governed by convection. Modeling cool stellar atmospheres requires a detailed treatment of the complex interplay between hydrodynamical flows and radiative cooling. CO5BOLD (COnservative COde for the COmputation of COmpressible COnvection in a BOx of L Dimensions, L=2,3) is one of the few radiation hydrodynamics codes designed specifically for realistic numerical simulations of the convective surface layers and atmospheres of cool stars. The resulting 3-dimensional (3D) model atmospheres are suitable for a direct comparison with real stellar atmospheres, and may be used for the calculation of synthetic spectra. Starting from the Sun, a grid of 3D CO5BOLD model atmospheres has been computed for solar-like stars with a wide range of metallicities. In addition, CO5BOLD has been used to study convection in stars as diverse as White Dwarfs, Brown Dwarfs, Red Giants, Supergiants, and AGB stars. Science applications range from the investigation of basic physical mechanisms responsible for wave excitation and heating stellar chromospheres to 3D corrections for spectroscopic abundance determinations. 3D non-LTE line formation has been applied to analyze the 6Li / 7Li isotopic ratio in metal-poor stars.