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**Theoretical atmosphere models provide the basis for a variety of applications for astronomy. In one-dimensional atmosphere models, convection is usually treated with the mixing-length theory. However, this theory is by far not flawless and the superadiabatic regime is poorly rendered. Due to the increasing computational power, 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 are currently computing the STAGGER grid, targeting 130 models, which will cover various evolutionary phases of cool stars. The effective temperature (Teff) ranges from 4000 to 6500 K in steps of 500 K, the surface gravity (logg) from 1.5 to 5.0 in steps of 0.5 dex and the metallicity ([Fe/H]) from 0.0 to -3.0 in steps of 1.0. In the course of my talk, I'll present you the current state of the grid, and I'll explore the differences between the mean 3D stratifications and corresponding 1D model atmospheres. Also, I'll elucidate our future-ambitions with the resulting grid models in the context of asteroseismology.**

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