The accumulation of damage due to localized corrosion [pitting, stress corrosion cracking (SCC), corrosion fatigue (CF), crevice corrosion (CC), and erosion-corrosion (EC)] in complex industrial systems, such as power plants, refineries, desalination systems, etc., poses a threat to continued safe and economic operation, primarily because of the sudden, catastrophic nature of the resulting failures. Of particular interest in managing these forms of damage is the development of robust algorithms that can be used to predict the integrated damage as a function of time and as a function of the operating conditions of the system. Because complex systems of the same design rapidly become unique, due to differences in operating histories, and because failures are rare events, there is generally insufficient data available on any given system to derive reliable empirical models that capture the impact of all (or even some) of the important independent variables. Accordingly, the models should be, to the greatest extent possible, deterministic with the output being constrained by the natural laws. In this paper, the theory of the initiation of damage, in the form of pitting, is briefly outlined. We then describe the deterministic prediction of the accumulation of damage from SCC and CF in Type 304 SS components in the primary coolant circuits of Boiling Water (Nuclear) Reactors (BWRs) and from pitting and SCC in low-pressure steam turbine disks. These cases have been selected to illustrate the various phases through which localized corrosion damage occurs.