We review the basic equations and corresponding variational formulations of the linearized vibrations of a liquid with a free surface contained in an elastic structure (hydroelasticity, sloshing, structural-acoustics).In hydroelastic standard situations, the liquid is considered as incompressible, gravity –sloshing effects being taken into account through appropriate fluid-structure interface operator referred as elastogravity operator using a scalar field (pressure and/or displacement potential fields for the fluid). Compressibility effects for the fluid can be introduced, neglecting gravity free surface effects as in structural-acoustic problems or taking them into account through some approximations. Recently, we have analysed on a rigorous manner the basic equations of compressibility/gravity interactions: the fluid irrotationality condition being replaced, in general, by a plane-irrotationality equation. We present here some basic appropriate corresponding variational formulations. Current investigations concern active/passive treatment for the vibration reduction as well as surface tension effects and various damping effects.