Cavitation erosion is one of the remarkable catastrophic consequences of cavitation. Predicting the cavitation aggressiveness quantitatively and predicting the most probable location of cavitation erosion are complex problems that currently still motivate an important amount of basic and applied research in the fields of hydrodynamics, physics and metallurgy. The work addresses two main issues: Numerical simulations of cavitating flows over hydrofoils; and an assessment of the risk of cavitation erosion on the surface of hydrofoils. The capability of the multiphase RANS method to predict the relevant and critical unsteady cavitation dynamics in the flow over hydrofoils has been investigated on two NACA hydrofoils (NACA0015 hydrofoil and NACA0018-45 hydrofoil) in the 2D and 3D domain, respectively. It was found that the large-scale structures and the typical unsteady cavitation dynamics predicted by the RANS method implemented in FLUENT were in fair agreement with the observations from experiments. To find the best criteria for an assessment of the risk of cavitation erosion, current erosion risk assessment models and methodologies that use computational fluid dynamic tools or experimental results as input were reviewed and evaluated. An erosion intensity function was proposed based on the mean value of those values of the time derivative of the local pressure that exceeds a certain threshold, and was evaluated for the NACA0015 hydrofoil and NACA0018-45 hydrofoil. A good correlation was found between the locations with the high erosion risk obtained from the computations and the damage area observed from paint tests.