  Advances in the fabrication and characterization of nanoscale systems now
allow for a deeper understanding of one of the most basic issues in science and
technology: the flow of energy at the microscopic level. In this Colloquium we
survey recent advances and present understanding of physical mechanisms of
energy transport in nanostructures, focusing mainly on molecular junctions and
atomic wires. We examine basic issues such as thermal conductivity,
thermoelectricity, local temperature and heating, and the relation between
energy current density and temperature gradient - known as Fourier's law. We
critically report on both theoretical and experimental progress in each of
these issues, and discuss future research opportunities in the field.
