In the recent years, materials with conical band structure have attracted much attention. There the electrons behave like relativistic particles, albeit moving hundreds of times slower than light. In graphene, a monoatomic layer of carbon, the conical electronic dispersion leads to the anomalous Hall effect, frequency-independent optical conductivity, giant Faraday effect, and marginal Fermi liquid behavior. Dirac dispersion in three-dimensional materials such as bismuth or cadmium arsenide causes large thermoelectric power, giant magneto-optical effects, and other functional properties. We explore the rich fundamental physics of these compounds, and the possibility of applications using optical (terahertz and infrared) spectroscopy.