The incorporation of NPs into polymers is a powerful strategy for improving their thermomechanical properties or for introducing new attributes (optical, electronic, magnetic, or catalytic properties) into otherwise inert polymers. The surfaces of the NPs are traditionally grafted with polymer ligands to stabilize NP dispersions in the host polymer, as the grafts introduce steric (entropic) repulsion between NPs that, if sufficiently large, can overcome the attractive interparticle forces that promote aggregation. However, emerging studies show that polymer grafting can also be used to direct NP assembly and access unique mesoscopic morphologies such as 1D strings and 2D sheets. These low-dimensional morphologies often exhibit functional properties very distinct from their 3D counterparts (superlattices, globular aggregates). For example, 1D fibrillar and string structures are the basis for colloidal NP gels that exhibit unique rheologies, low percolation thresholds, and high porosities, enabling the synthesis of functional materials such as hydrogels that exhibit reversible sol-gel transitions and metallic aerogels that exhibit high electrocatalytic activity. Noble metal NPs that are assembled into periodic 1D and 2D architectures are known to support collective optical modes as a result of plasmonic coupling , resulting in subwavelength light confinement, nanoscale waveguiding, and topological plasmonic edge states. Polymer grafting has the potential to program assembly in 1D and 2D morphologies as well as control the separation distance and relative orientation (for shaped NPs) between adjacent NPs within the assemblies, both of which are critical for the function of these NP-based assemblies. These highly anisotropic assembly morphologies are a direct manifestation of how polymergrafted NPs interact with each other but are difficult to predict. Spherical, uniformly grafted NPs exhibit isotropic two-body interactions, which predict the formation of isotropic NP assemblies.