Several reduced order formulations are reviewed in the case of linear vibration analysis of bounded fluid-structure systems for low modal density situations. Compressibility effects in the fluid for interior structural-acoustic problems, and free-surface gravity effects, as well as for hydroelastic-sloshing interaction problems in the case of incompressible liquids, are examined. Reduced order models leading to symmetric matrix systems are then described using static well-posed behavior of the irrotational fluid. In this respect, the fluid-structure boundary value local equations, expressed in terms of fluid scalar field variables for the fluid (and displacement variables for the structure), are regularized for zero-frequency limit.