This Centennial Feature Article provides an overview of research in the general area of self-assembly modeling, with particular emphasis on the self-assembly of molecules into soft nanoscale structures where the driving force for assembly is provided by nonbonded interactions (hydrogen bonds and electrostatics). The models have been developed at many different levels of theory, going all the way from simple analytical models of packing effects to atomistic descriptions using molecular dynamics methods. In between these limits are mean-field and coarse-grained models, including models for DNA, peptides, and lipids that can be used to describe the assembly of hybrid (amphiphilic) materials. Several recent applications to specific systems are discussed, including the description of peptide amphiphile assembly to make cylindrical micelles, the assembly and melting of DNA hairpins, the use of DNA tethers to assemble nanoparticles into aggregates and crystalline structures, and the use of coarse-grained lipid models to make lamellar and high-curvature phases. These examples demonstrate the difficulties associated with brute force atomistic methods, and they also show the opportunities (but uncertainties and ambiguities) associated with simpler models such as coarse-grained models. The examples also demonstrate the usefulness of successful modeling methods in the design of new materials, including an understanding of the relationship between structure and function.