Insulators and polymer-coated insulators are provided. The insulators can include thermally-insulating nanoparticles and a binder configured to volatilize at a volatilization temperature. Insulators can also include an inorganic thermally-insulating material forming a porous structure. The porous structure can be configured to reduce the mean free path of gases in the insulator as compared to gases outside the porous structure. Polymer-coated insulators including an inorganic thermally-insulating material and a polymer coating disposed on the surface of the inorganic thermally-insulating material are also provided. Insulators can also include thermally-insulating nanoparticles and an opacifier. The opacifier can include a carbonaceous material coated with a refractory material that inhibits oxidation of the carbonaceous material at a carbon oxidation temperature. The insulators or polymer-coated insulators can be disposed between battery cells or battery cell blocks in an apparatus.