Theoretical atmosphere models provide the basis for a variety of applications in astronomy. In simplified one-dimensional (1D) atmosphere models, convection is usually treated with the mixing length theory despite its well-known insufficiency, therefore, the superadiabatic regime is poorly rendered. Due to the increasing computational power over the last decades, we are now capable to compute large grids of realistic three-dimensional (3D) hydrodynamical model atmospheres with the realistic treatment of the radiative transfer. We have computed the Stagger-grid, a comprehensive grid of 3D atmosphere models for late-type stars. In the presented contribution, we discuss initial results of the grid by exploring global properties and mean stratifications of the 3D models. Furthermore, we also depict the differences to classic 1D atmosphere models.