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Amphiphilic materials can assemble into a wide variety of morphologies and have emerged as a novel class of candidates for drug delivery. Along with a large number of experiments reported, computational studies have been also conducted in this field. At an atomistic/molecular level, computations can facilitate quantitative understanding of experimental observations and secure fundamental interpretation of underlying phenomena. This review summarizes the recent computational efforts on amphiphilic copolymers and peptides for drug delivery. Atom-resolution and time-resolved insights are provided from bottom-up to microscopically elucidate the mechanisms of drug loading/release, which are indispensable in the rational screening and design of new amphiphiles for high-efficacy drug delivery.