In this talk I will present recent theoretical and numerical progress in modeling the dynamics of stratified turbulence in regimes appropriate of the Earth's atmosphere and oceans, of the interiors of giant planets, and of stellar interiors. Multiscale asymptotic analysis reveals the existence of several different dynamical regimes, each with its own specific set of scaling laws relating the turbulence properties to the stratification. Direct Numerical Simulations are then used to test and validate these model predictions.