This brief review of the tunnelling-state model explains the observed low-temperature thermal properties of amorphous materials. Below 1.0 K, the amorphous materials have, over and above contribution by phonons, a specific heat capacitycthat varies almost linearly with temperature; and the thermal conductivitykis approximately proportional toT2, becoming almost independent ofTabove 1.0 K. This behaviour is very different from that of crystalline materials, for whichcαT3andkαT3in this range. A broad band of localized excitations is apparently an intrinsic characteristic of the amorphous state. The tunnelling-state model for these localized excitations can explain qualitatively the various unusual low-temperature properties found in amorphous materials, even though no physical description of the tunnelling entity for any material is available.