The existing measurements and theories of the low-temperature thermal properties, heat capacity, and thermal conductivity of polymers are reviewed with particular attention paid to the differences between partly crystalline and amorphous polymers. The most striking feature of the low-temperature heat capacity of polymers is that in the liquid helium temperature range the heat capacity does not depend upon the cube of the temperature as for other solids. Further, only well below 1°K does the heat capacity approach the value predicted on the basis of the sound velocity. This behavior indicates the presence of a small number of low-frequency modes of vibration in the frequency spectrum. The fact that such anomalous behavior seems linearly related to the crystallinity implies that this behavior is associated with the amorphous structure, perhaps with motions of pendent groups within cavities formed in the amorphous structure. The thermal conductivity of semicrystalline and amorphous polymers differs considerably. Semicrystalline polymers display a temperature dependence of the thermal conductivity similar to that obtained from highly imperfect crystals, the thermal conductivity having a maximum in the temperature range near 100°K which moves to lower temperatures and higher thermal conductivities as the crystallinity is increased. Amorphous polymers display a temperature dependence similar to that obtained for glasses with no maximum but a significant plateau region in the range between 5 and 15°K. The theoretical interpretation of the thermal conductivity of these materials is considered.