The development of high-performance polymeric materials typically involves a trade-off between desirable properties such as processability, recyclability, durability, and strength. Two common strategies in this regard are composites and reversibly cross-linked materials. Making optimal choices in the vast design spaces of these polymeric materials requires a solid understanding of the molecular-scale mechanisms that determine the relation between their structure and their mechanical properties. Over the past few years, a wide range of computational techniques has been developed and employed to model these mechanisms and build this understanding. Focusing on approaches rooted in molecular dynamics, we present and discuss these techniques, and demonstrate their use in several physical models of novel polymer-based materials, including nanocomposites, toughened gels, double network elastomers, vitrimers, and reversibly cross-linked semiflexible biopolymers.