The durability of natural glasses on geological time scales and ancient glasses for thousands of years is well documented. The necessity to predict the durability of high-level nuclear waste (HLW) glasses on extended time scales has led to various thermodynamic and kinetic approaches. Advances in the measurement of medium-range order in glasses has led to the understanding that the molecular structure of a glass, and thus the glass composition, controls the glass durability by establishing the distribution of ion exchange sites, hydrolysis sites, and the access of water to those sites. During the early stages of glass dissolution, a “gel” layer resembling a membrane forms through which ions exchange between the glass and the leachant. The hydrated gel layer exhibits acid/base properties, which are manifested as the pH dependence of the thickness and nature of the gel layer. The gel layer ages into clay or zeolite minerals by Ostwald ripening. Zeolite mineral assemblages (higher pH and Al3+ rich glasses) may cause the dissolution rate to increase, which is undesirable for long-term performance of glass in the environment. Thermodynamic and structural approaches to the prediction of glass durability are compared versus Ostwald ripening.