Macroscopic properties of polymer nanocomposites depend on the microscopic composite morphology of the constituent nanoparticles and polymer matrix. One way to control the spatial arrangement of the nanoparticles in the polymer matrix is by grafting the nanoparticle surfaces with polymers that can tune the effective interparticle interactions in the polymer matrix. A fundamental understanding of how graft and matrix polymer chemistries and molecular weight, grafting density, and nanoparticle size, and chemistry affect interparticle interactions is needed to design the appropriate polymer ligands to achieve the target morphology. Theory and simulations have proven to be useful tools in this regard due to their ability to link molecular level interactions to the morphology. In this feature article, we present our recent theory and simulation studies of polymer grafted nanoparticles with chemical and physical heterogeneity in grafts to calculate the effective interactions and morphology as a function of chemistry, molecular weights, grafting densities, and so forth.