Understanding corrosion of nuclear waste glasses in aqueous environments is critical to the assessment of effeteness of these materials as a medial to immobilize medium and high level nuclear wastes. Despite advances of analytical techniques that provide a wealth of information of water-glass interactions, there remain many unanswered questions in fundamental steps and mechanisms. In this talk, I will introduce applications of atomistic simulation methods in understanding of the glass-water interaction and corrosion behaviors of silicate and borosilicate nuclear waste glasses. Starting from generation of accurate structural models of multicomponent borosilicate nuclear waste glasses using molecular dynamics simulations, particularly recent development of interatomic potentials that enable these simulations, glass surface-water interactions from simulations using reactive potentials will be then presented. Quantitative Structure-Property Relationship analysis based on structural features from these simulations and its usage to correlate with measured dissolution rates will be discussed. Dissolution gel layer formation as a result of glass corrosion and related structural and transport behaviors from atomistic simulations will also be discussed.