This chapter considers thermal conductivities of gases and then of solids. Thermal conductivity determines whether a material feels hot or cold to the touch, and why some materials are good thermal insulators while others efficiently conduct heat. As for electrical conductivity, the values of thermal conductivity can vary by orders of magnitude from one material to another and even within a given material when the temperature is changed. Thermally insulating tiles play an important role in protecting space vehicles as they pass through the atmosphere. Most of the tiles are made of amorphous silica fibers. The fact that they are amorphous means that they are poor conductors of heat, as such materials have very short phonon mean free paths due to the lack of a periodic structure. The tiles are prepared by making water slurry of the fibers, casting it into soft blocks to which colloidal silica binder has been added, and then sintering at high temperature.