Desalination and water reuse are rapidly evolving technologies that have become mainstays of a broad portfolio of water management practices around the globe. Osmotically-driven molecular partitioning processes mediated by functional permselective membranes lay at the heart of each of these technologies. Despite a strong theoretical and empirical framework of knowledge discovered over the past half century that allows engineering of modern reverse osmosis (RO) systems at unprecedented scales, our understanding of water transport and solute rejection at the atomic and molecular scales by the semipermeable membranes is incomplete. One reason for this is a dearth of analytical techniques capable of non-invasively accessing (and visualizing) in real time the exceedingly small spatial and temporal dimensions of atomic interactions underlying membrane transport phenomena. This knowledge gap has been increasingly eroded, however, since the first use of molecular simulations to explore RO membrane structure and dynamics in the late 1990s. Over the last decade, molecular dynamics (MD) and related simulations techniques have been aggressively pursued to advance understanding of membrane architecture and transport at the atomistic scale. Results emerging from sophisticated computational approaches, especially when coupled with today's powerful new imaging technologies, reveal a rich landscape of physicochemical interactions not only inside the polymer membranes, but also at the water-membrane interface. For example, it is now clear that the discriminating polyamide (PA) layer of modern RO membranes consists of an inhomogeneous tangled polymer network pervaded by tortuous water-filled transmembrane "tunnels" and nanopores whose shapes fluctuate at ambient temperatures over femtosecond to picosecond time scales. Recent modeling efforts indicate that the nanoscale roughness of PA membranes, evident in electron micrographs, is also reflected at the atomic scale, with an illdefined diffuse interfacial region shared with the bulk water phase. Simulations are also yielding a clearer picture of water and solute (ions and small organics) behaviors inside the membrane matrix resulting from complex intermolecular hydrogen bonding and atomistic solvation processes. The thermodynamic (enthalpy and free-energy) barriers to water and solute entrance into nanopores located at membrane surfaces have been recently elucidated by means of specialized non-equilibrium simulations protocols. Notwithstanding these recent successes, questions nonetheless remain concerning membrane molecular organization and performance, especially with respect to their ability to reject certain small organic compounds and not others. Other questions concern the dynamic interplay between membrane surfaces and foulant molecules as they undergo adsorption. Because of its unique ability to translate atomic-scale interactions and processes into a dynamic visual experience, it is anticipated that computational chemistry will play an ever greater role in the coming years in helping to answer these and related questions about membrane structure and function. It is expected that fundamental advancements in these areas will lead to a new generation of membrane materials with improved durability and reduced energy demands.