Recent breakthrough in fabrication of graphene and its derived nanostructures has opened the way for fundamental study of novel thermal transport phenomena at nanoscale.In this talk,I will present the results of our systematic study based on the non-equilibrium Greens function method for understanding the thermal transport properties in graphene and its derived nanostructures [1-9],focusing on(a)effects of isotopic superlattice modulation in graphene nanoribbons [1];(b)effects of thermal rectification in asymmetric three-terminal graphene nanojunctions [2];(c)thermal conductance modulators based on folded or arched graphene nanoribbons [3,4];(d)thermal transport in hexagonal boron nitride nanoribbons;(e)thermal transport in graphyne nanoribbons [7];(f)thermoelectric properties of hybrid graphene/boron nitride nanoribbons [8];(g)phonon resonant splitting in T-shaped graphene nanoribbons [9].