We review dynamic processes in supercooled liquids and glasses as studied by dielectric spectroscopy. It is the only experimental technique which allows one to follow the tremendous slow-down of diffusive motion of particles in disordered condensed matter over more than 18 decades in frequency or time. The dielectric techniques used are treated in detail. As an introduction for non-specialists, the time and temperature evolution of the basic spectral features associated with various dynamic relaxation processes are discussed in detail. Among them are the structural relaxation, the occurrence of fast processes and the boson peak. The relevance of these features for glass formation is discussed. The present article may also serve as a review for recent experimental and theoretical studies on glass-forming liquids.