Abstract: Heat dissipation is a key challenge in the development of nanoscale devices. In this paper we describe the state-of-the-art of nanoscale devices and some fundamental issues of nanoscale thermal conduction, using carbon nanotubes and graphene as examples.We then present various new interesting phenomena in this field.We also discuss the main physical mechanisms that influence the thermal conductivity of nanomaterials.An understanding of thermal conduction in low-dimensional systems is not only of fundamental interest in physics, but is also of great relevance to the development of nanoscale electronics, with a broad range of future applications.