Transient absorption microscopy is an experimental technique that allows nanomaterials to be studied with ultrafast time resolution and diffraction limited spatial resolution. This paper describes recent results from using transient absorption microscopy to investigate energy relaxation processes in single metal and semiconductor nanowires. The processes that have been examined include charge carrier trapping in semiconductor nanostructures, the motion of surface plasmon polaritons in metal nanowires, and the damping of the acoustic breathing modes of metal nanowires by high viscosity solvents.