Modern computational methods have proved invaluable for the design and analysis of structural components using lightweight materials. The challenge of optimizing lightweight materials in the design of industrial components relates to incorporating structure-property relationships within the computational strategy to incur robust designs. One effective methodology of incorporating structure-property relationships within a simulation-based design framework is to employ a hierarchical multiscale modeling strategy. This paper reviews techniques of multiscale modeling to predict the mechanical behavior of amorphous polymers. Hierarchical multiscale methods bridge nanoscale mechanisms to the macroscale/continuum by introducing a set of structure-property relationships. This review discusses the current state of the art and challenges for three distinct scales: quantum, atomistic/coarse graining, and continuum mechanics. For each scale, we review the modeling techniques and tools, as well as discuss important recent contributions. To help focus the review, we have mainly considered research devoted to amorphous polymers.