Geophysical fluid dynamics consider domains with horizontal length scales much larger than the vertical ones. In this regime, simplified mathematical models based on the hydrostatic approximation can be derived rigorously, such as the classical shallow water equations. Furthermore, vertically averaged or multi-layer non-hydrostatic models can also be derived in order to reproduce dispersive effects. In this talk, the classical derivation of shallow water models will be reviewed critically, with special focus on the role of turbulence modelling, on the choice of the proper time scales, on the treatment of boundary conditions at the free surface and on the correct asymptotic procedure to be followed, in order to provide a more solid foundation to the rigorous derivation of simplified models including non-hydrostatic pressure terms.