Phonons are primary heat carriers in carbon nanotubes (CNTs) and graphene; a fundamental understanding of phonon transport in these nano-structures is required for the energy efficient design of their devices such as integrated circuit, flexible displays, and transparent electrodes. In this work, atomistic simulations have been performed to investigate thermal transport at interfaces of CNT and graphene that are typically encountered in their applications, e.g., CNT-CNT junctions on silicon oxide substrate, interfaces between shells of double-wall CNTs (DWNTs), and graphene-metal interfaces. Firstly, heat dissipation at CNT junctions supported on the silicon dioxide substrate is investigated using molecular dynamics (MD) simulations and methods for phonon spectrum analysis. The results show the inefficient heat removal from CNTs not making direct contact with the oxide substrate is responsible for the breakdown of CNT network. At interfaces between shells of DWNTs, the radial vibration modes are identified as phonons that are strongly coupled and can efficiently exchange energy between shells of DWNTs. Secondly, the thermal conductivity of suspended single layer graphene (SLG) and SLG supported on Cu is determined using equilibrium MD simulations following Green-Kubo method and relaxation time approximation approach at room temperature. It is demonstrated that the interaction with Cu substrate can significantly reduce the thermal conductivity of SLG, and that the reduction of thermal conductivity from three acoustic phonons is the major reason. Lastly, using atomistic Green’s function method and density function theory calculations, the thermal boundary conductance at interfaces across graphene layers sandwiched by different metals including Cu, Au, and Ti is predicted. The work shows how the bonding strength changes the graphene/metal and graphene/graphene phonon coupling, and demonstrated the transition of thermal transport mechanism from metal/graphene dominated resistance to graphene/graphene dominated resistance as the metal/graphene bonding strength increases in metal/MLG/metal structure.