Contact thermal resistance between individual nanostructures plays an important role in thermal management of nanoelectronic devices and thermal transport of nanocomposites. However, experimental data of thermal resistance of these nanoscale contacts are very limited because of the experimental challenges. Recently we have developed an approach to directly measure the contact thermal resistance between individual nanostructures. Here we report on measurement results of contact thermal resistance between individual multi-walled carbon nanotubes, surface modified carbon nanotubes, carbon nanotubes and gold nanowires, and carbon nanotubes and boron nitride nanotubes. These studies involve phonon scattering at hard-soft materials interface, electron-phonon coupling, and acoustic impedance mismatch. Analyses of experimental data yield new insights into contact thermal resistance between nanostructures and provide guidelines for designing nanoscomposites with tunable thermal properties.