Glasses and amorphous materials strongly differ in their dynamic properties from their crystalline counterparts. In crystals the typical excitations are the phonons. In glasses disorder reduces the mean free path of all but the longest wavelength phonons so strongly that it drops below their wavelength. The vibrations can then no longer be described meaningfully by extended phonons. The vibrational spectrum, however, still resembles the one of the ordered, crystalline structures. Typical for glasses are - coexisting with the long wavelength phonons (sound waves) - additional low energy excitations: tunneling, soft localized vibrations and relaxations. These can be described by the soft potential model which postulates a common origin of these additional excitations and is, for very low temperatures (typically T < 1 K), equivalent to the well known tunneling model. From general properties of the distribution functions describing the soft potentials one derives the temperature dependencies of quantities such as the specific heat or the thermal conductivity. These universal relations hold to about T = 10 K. From fits of the model to the experimental data one finds that 20-100 atoms participate in the excitation modes. Computer simulations are used to test the assumptions of the model and to provide some insight into the microscopic origin of the modes. One finds soft vibrational modes, as well as relaxations, concentrated on 10 or more atoms. These modes are centred at structural irregularities.