Thermal transport in graphene and graphene nanostructures have been studied experimentally and theoretically. Methods and previous work to measure and calculate the thermal conductivities of graphene and related nanostructures are briefly reviewed. We demonstrate that combining Raman spectroscopy for thermometry and electrical transport for Joule heating is an effective approach to measure both graphene thermal conductivity and graphene-substrate interface thermal resistance. This technique has been applied to a variety of exfoliated or CVD-grown graphene samples (both suspended and substrate-supported), yielding values comparable with those measured using all-optical or all-electrical techniques. We have also employed classical molecular dynamics simulation to study thermal transport in graphene nanostructures and suggest such structures may be used as promising building blocks for nanoscale thermal engineering. ©The Electrochemical Society.