Cu/SSZ-13 Selective Catalytic Reduction (SCR) catalysts have been extensively studied for the past five-plus years. New and exciting fundamental and applied science has appeared in the literature quite frequently over this time. In this short review, a few topics specifically focused on a molecular-level understanding of this catalyst are summarized: (1) The nature of the active sites and, in particular, their transformations under varying reaction conditions that include dehydration, the presence of the various SCR reactants and hydrothermal aging; (2) Discussions of standard and fast SCR reaction mechanisms. Considerable progress has been made, especially in the last couple of years, on standard SCR mechanisms. In contrast, mechanisms for fast SCR are much less understood. Possible reaction paths are hypothesized for this latter case to stimulate further investigations; (3) Discussions of rational catalyst design based on new knowledge obtained regarding catalyst stability, overall catalytic performance and mechanistic catalytic chemistry.