Fluid-structure vibrations occur in various situations, in aerospace, automotive, civil engineering areas as well as in biomechanics. For a general overview of aerospace interior fluid-structure problems, we refer for instance the reader to Abramson, 1966. The computational aspects concerning the linear vibratory response of fluid-structure systems to prescribed loads may lead, for complex structures, to a prohibitive number of degrees of freedom. In order to quantify the weak or strong interactions of the coupled fluid-structure system, in order to carry out sensitivity analysis, in order to introduce interface appropriate active/passive damping treatment (intelligent adaptive fluid-structure systems), reduced order procedures are required. That is why concepts which have been introduced for structural dynamics, such as component mode synthesis, are presently revisited and adapted to some multiphysic problems. We review in this paper reduced order models for modal analysis of elastic structures containing an inviscid fluid (gas or liquid). These methods, based on Ritz-Galerkin projection using appropriate Ritz vectors, allow us to construct reduced models expressed in terms of physical displacement vector field u in the structure, and generalized displacement vector r describing the behaviour of the fluid. Those reduced models lead to unsymmetric (Craggs and Stead, 1976; Sung and Nefske, 1986) or symmetric generalized eigenvalue matrix system (Morand and Ohayon, 1979, 1995; Ohayon, 2001) involving a reduced number of degrees of freedom for the fluid. For this purpose, we construct symmetric matrix models of the fluid considered as a subsystem, by considering the response of the fluid to a prescribed normal displacement of the fluid-structure interface. Two distinct situations are analyzed. On one hand, we consider linear vibrations of an elastic structure completely filled with a compressible gas or liquid and on the other hand, we consider the case of an elastic structure containing an incompressible liquid with free surface effects due to gravity. The first case is a structural acoustic problem. In the case of a structure containing a gas, we consider a modal interaction between structural modes in vacuo and acoustic modes in rigid motionless cavity. For a structure containing a compressible liquid, we consider a modal interaction between hydroelastic modes including ”static” inertial and potential compressibility effects and acoustic modes in rigid motionless cavity. Interface local fluid-structure dissipation through a local wall impedance can also be introduced easily in the formulations. The second case is a hydroelastic-sloshing problem with a modal interaction between incompressible hydroelastic structural modes with incompressible liquid sloshing modes in rigid motionless cavity, involving an elastogravity operator related to the wall normal displacement of 2 the fluid-structure interface, introduced initially, under a simplified approximate expression by Tong, 1966, then analyzed through various derivations by Morand and Ohayon, chapter 6, 1995 and recently deeply analyzed theoretically and numerically by Schott´e in his PhD dissertation (Schott´e and Ohayon, 2003, 2005). For the construction of reduced models, the static behavior at zero frequency play an important role. Therefore, we review “regularized” variational formulations of the problem, in the sense that the static behaviour must also be in taken into account in the boundary value problem. Those “quasi-static” potential and inertial contributions plays a fundamental role in the Ritz-Galerkin procedure (error truncation). The general methodology corresponds to dynamic substructuring procedures adapted to fluid-structure modal analysis. For general presentations of computational methods using appropriate finite element and dynamic substructuring procedures applied to modal analysis of elastic structures containing inviscid fluids (sloshing, hydroelasticity and structural-acoustics), we refer the reader for instance to Morand and Ohayon 1995.