It is shown how the standard RSW can be ’augmented’ to include phase transitions of water. This chapter explains how to incorporate extra (convective) vertical fluxes in the model. By using Lagrangian conservation of equivalent potential temperature condensation of the water vapour, which is otherwise a passive tracer, is included in the model and linked to convective fluxes. Simple relaxational parameterisation of condensation permits the closure of the system, and surface evaporation can be easily included. Physical and mathematical properties of thus obtained model are explained, and illustrated on the example of wave scattering on the moisture front. The model is applied to ’moist’ baroclinic instability of jets and vortices. Condensation is shown to produce a transient increase of the growth rate. Special attention is paid to the moist instabilities of hurricane-like vortices, which are shown to enhance intensification of the hurricane, increase gravity wave emission, and generate convection-coupled waves.