Nanocomposites consist of graphene dispersed in matrices of soft materials are promising thermal management materials. A fundamental understanding of the thermal transport at graphene-soft material interfaces is essential for developing these nanocomposites. In this dissertation, thermal transport at graphene-octane interfaces was investigated using molecular dynamics simulations, and the results revealed several important characteristics of such thermal transport. The interfacial thermal conductance of graphene-octane interfaces were studied first. It was found that the interfacial thermal conductance exhibits a distinct duality: if heat enters graphene from one side of its basal plane and leaves it through the other side, the corresponding interfacial thermal conductance, Gacross, is large; if heat enters graphene from both sides of its basal plane and leaves it at a position far away on its basal plane, the corresponding interfacial thermal conductance, Gnon-across, is small. Gacross is ~30 times larger than Gnon-across for a single-layer graphene immersed in liquid octane. Additional analysis showed that this duality originates partially from the strong, positive correlations between the heat fluxes at the two surfaces of a graphene layer. The interfacial thermal conductance of the graphene-soft material interfaces in presence of defects in the graphene was then studied. The results showed that the heat transfer at the interfaces is enhanced by defects. Estimations based on effective medium theories showed that the effective thermal conductivity of the graphene-based composites could even be enhanced with defects in graphene when heat transfer at the graphene-soft material interface is the bottleneck for the thermal transport in these composites. To describe the interfacial thermal transport at graphene interfaces uniformly, a nonlocal constitutive model was proposed and validated to replace the classical Kapitza model. By characterizing the thermal transport properties of graphene interfaces using a pair of thermal conductance, the model affords a uniform description of the thermal transport at graphene interfaces for different thermal transport modes. Using this model, the data interpretation in time domain thermalreflectance (TDTR) measurements was investigated, and the results showed that the interfacial thermal conductance measured in typical TDTR tests is that of the across mode for thin-layered materials. / Ph. D.