The disposal of high-level radioactive waste (HLW) and spent nuclear fuel (SF) presents a unique challenge for the prediction of the long-term performance of corrodible structures since HLW/SF containers are expected, in some cases, to have lifetimes of one million years or longer. Various empirical and deterministic models have been developed over the past 45 years for making predictions of long-term corrosion behaviour, including models for uniform and localised corrosion, environmentally assisted cracking, microbiologically influenced corrosion, and radiation-induced corrosion. More recently, fracture-mechanics-based approaches have been developed to account for joint mechanical–corrosion degradation modes. Regardless of whether empirical or deterministic models are used, it is essential to be able to demonstrate a thorough mechanistic understanding of the corrosion processes involved. In addition to process models focused on specific corrosion mechanisms, there is also a need for performance-assessment models as part of the overall demonstration of the safety of a deep geological repository. Performance-assessment models are discussed in Part 2 of this review.