Tunneling states in amorphous solids are shown to explain the linear temperature dependence of specific heat at very low temperatures. This model also predicts the observed temperature dependence and magnitude of thermal conductivity, and explains anomalous results for phonon free path via stimulated Brillouin scattering. Recent experiments on vitreous silica, germania, and selenium between 70 mK and 1 K highlight the incomplete understanding of low-temperature thermal properties of amorphous solids. These experiments confirm a linear temperature-dependent term in specific heat, with a magnitude of ~10^-6 TJ(g·K^-1) in all three materials. A previous theory suggests this term arises from a quasimetallic contribution due to energy band tails in disordered semiconductors, but it fails to explain the T^1.8 dependence of thermal conductivity below 1 K and may not apply to materials with larger energy gaps. An alternative model based on tunneling states is proposed, which explains and links observed specific heat and thermal conductivity. Tunneling states are known in alkali halides and recently reported in polyethylene. In polyethylene, the relaxation time was successfully interpreted by considering a particle in an asymmetric one-dimensional potential well. This model is extended to completely amorphous materials, calculating the contribution of tunneling states to specific heat and thermal conductivity. It is noted that Anderson et al. are developing a similar model. Tunneling states have been suggested as the origin of excess specific heat in fused silica above 1 K, but this model predicts the wrong sign for the Gruneisen constant, which is attributed to the specific model chosen. The behavior of specific heat on neutron irradiation indicates the anomaly above 1 K is distinct from that below. The paper focuses on temperatures below 1 K. Section 2 describes the model, focusing on the energy distribution of tunneling states, and calculates their contribution to thermal properties, comparing with experimental results. Section 4 reconciles phonon mean free path values from Brillouin scattering with those from thermal conductivity. The microscopic origin of these states is speculated.Tunneling states in amorphous solids are shown to explain the linear temperature dependence of specific heat at very low temperatures. This model also predicts the observed temperature dependence and magnitude of thermal conductivity, and explains anomalous results for phonon free path via stimulated Brillouin scattering. Recent experiments on vitreous silica, germania, and selenium between 70 mK and 1 K highlight the incomplete understanding of low-temperature thermal properties of amorphous solids. These experiments confirm a linear temperature-dependent term in specific heat, with a magnitude of ~10^-6 TJ(g·K^-1) in all three materials. A previous theory suggests this term arises from a quasimetallic contribution due to energy band tails in disordered semiconductors, but it fails to explain the T^1.8 dependence of thermal conductivity below 1 K and may not apply to materials with larger energy gaps. An alternative model based on tunneling states is proposed, which explains and links observed specific heat and thermal conductivity. Tunneling states are known in alkali halides and recently reported in polyethylene. In polyethylene, the relaxation time was successfully interpreted by considering a particle in an asymmetric one-dimensional potential well. This model is extended to completely amorphous materials, calculating the contribution of tunneling states to specific heat and thermal conductivity. It is noted that Anderson et al. are developing a similar model. Tunneling states have been suggested as the origin of excess specific heat in fused silica above 1 K, but this model predicts the wrong sign for the Gruneisen constant, which is attributed to the specific model chosen. The behavior of specific heat on neutron irradiation indicates the anomaly above 1 K is distinct from that below. The paper focuses on temperatures below 1 K. Section 2 describes the model, focusing on the energy distribution of tunneling states, and calculates their contribution to thermal properties, comparing with experimental results. Section 4 reconciles phonon mean free path values from Brillouin scattering with those from thermal conductivity. The microscopic origin of these states is speculated.