Nanomedicine employs molecular materials for prevention and treatment of disease. Recently, smart nanoparticle (NP)-based drug delivery systems were developed for the advanced transport of drug molecules. Rationally engineered organic and inorganic NP platforms hold the promise of improving drug targeting, solubility, prolonged circulation, and tissue penetration. However, despite great progress in the synthesis of NP building blocks, more interdisciplinary research is needed to understand their self-assembly and optimize their performance as smart nanocarriers. Multi-scale modeling and simulations provide a valuable ally to experiment by mapping the potential energy landscape of self-assembly, translocation, and delivery of smart drug-loaded NPs. Here, we highlight key recent advances to illustrate the concepts, methods, and applications of smart polymer-based NP drug delivery. We summarize the key design principles emerging for advanced multifunctional polymer topologies, illustrating how the unusual architecture and chemistry of dendritic polymers, self-assembling polyelectrolytes and cyclic polymers can provide exceptional drug delivery platforms. We provide a roadmap outlining the opportunities and challenges for the effective use of predictive multiscale molecular modeling techniques to accelerate the development of smart polymer-based drug delivery systems.