Abstract : This manuscript is devoted to the modelling of water waves in the deep water regime with some emphasis on the underlying variational structures. The present article should be considered as a review of some existing models and modelling approaches even if new results are presented as well. Namely, we derive the deep water analogue of the celebrated Serre-Green-Naghdi equations which have become the standard model in shallow water environments. The relation to existing models is discussed. Moreover, the multi-symplectic structure of these equations is reported as well. The results of this work can be used to develop various types of robust structure-preserving variational integrators in deep water. The methodology of constructing approximate models presented in this study can be naturally extrapolated to other physical flow regimes as well.