This article summarizes the present state of knowledge concerning aqueous alteration of R7T7-type nuclear containment glasses, represented mainly by the inactive reference glass designated SON68. Based on this review, we propose to describe the glass alteration kinetics up to and including the final residual rate regime by means of a new mechanistic model known as GRAAL (glass reactivity with allowance for the alteration layer). Phenomenological analysis findings are reviewed for the various glass alteration regimes: interdiffusion, initial rate, rate drop, residual rate and, under very particular circumstances, resumption of alteration. These alteration regimes are associated with predominant mechanisms. Published work interpreting and modeling these mechanisms was examined in detail. There is a broad consensus on the general mechanisms of the initial rate and even the interdiffusion regime, whereas the mechanisms controlling the rate drop remain a subject of dispute not only with regard to nuclear glasses but also for the dissolution of silicate minerals. The reaction affinity responsible for the rate drop is expressed differently by different authors and depending on the underlying theories. The disagreement concerns the nature of the phase (glass or gel) or the activated complex controlling the rate drop, which in turn determines the elements that must be taken into account in the overall affinity term. Progress in recent years, especially in identifying the mechanisms responsible for the residual rate, has shed new light on these issues, allowing us to propose new theoretical foundations for modeling the different kinetic regimes of SON68 nuclear glass dissolution. The GRAAL model considers that water diffusion in the passivating reaction zone (the gel formed under saturation conditions) is a rate-limiting step in the overall glass dissolution kinetics. Moreover, this passivation zone is a soluble phase whose stability is directly dependent on the nature of the secondary phases likely to precipitate and on the solution renewal conditions.