The numerical simulation of steady and unsteady cavitating flows presents unique challenges in the development of robust numerical methodologies. The major difficulties are associated with the large density variations due to the phase change processes, and the modeling of liquid-vapor mass transfer (along with potentially strong interfacial heat transfer). The multiphase cavitation modeling approach described in this paper has been found to be capable of addressing these issues in an accurate and robust fashion, and is therefore suitable for inclusion in an advanced general purpose CFD solver. In the present approach, cavitation can be modeled within the framework of either the multiphase mixture model or the Eulerian multifluid model. The governing equations are the mixture (mixture model) or phase (Eulerian multifluid model) momentum, energy, turbulence, and phase volume fraction equations. The liquid-vapor mass transfer (evaporation and condensation) is modeled using two baseline cavitation models: Schnerr-Sauer model, and Zwart-Gerber-Belamri model. An advanced numerical scheme has been developed for solving the model equations which can handle large liquid-vapor density ratios, provide for mass transfer source terms in phase volume equations, and address the coupling between the phase change rates and the pressure correction equation. In addition, the cavitation models have been extended to compressible multiphase liquid and vapor flow regimes, and to problems involving convective heat transfer. The numerical algorithm has been implemented in an advanced, general-purpose CFD code, FLUENT, and validations have been carried out for a range of steady-state and unsteady flows, including a 2D axisymmetric orifice, a 3D fuel injector, a radial liquid pump, and a vane pump. The results demonstrate that the cavitation models are able to correctly predict the location and size of vapor bubbles, pressure distributions, and bulk flow parameters. Tests also indicate that the present implementation is both fast and robust, as compared to previous approaches. For unsteady simulations, the method can employ large time steps (limited only by physical or mesh motion considerations), making it efficient for unsteady flows driven by either boundary conditions or mesh motion.