2D and 3D Dirac materials have been intensively studied for the last 15 years. They are characterized by the fact that the dispersions of conduction electrons resemble the dispersion of relativistic Dirac electrons. Since the discovery of the first Dirac materials, great attention has been devoted to the explanation of their transport and optical properties. In this thesis, the optical properties of 2D and 3D Dirac systems are studied in detail. Hexagonal boron nitride is an example of a 2D system with finite Dirac mass, and Bi_2Se_3 is a typical 3D Dirac semimetal. For those two examples, the calculation of the elements of the conductivity tensor is performed by using the relaxation time approximation. The dependences of the conductivity tensor on various parameters, on doping, on the interband gap and on relaxation times, are determined. In typical Dirac semimetals, the low-energy optical conductivity consists of intraband and interband contributions. The intraband contributions are found to have simple dependences on the doping level and on the value of the interband gap. The interband contributions, on the other hand, have dependences on the model parameters that agree well with the results of measurements on different 3D Dirac materials. In this thesis, it is shown that the temperature dependence of the interband optical conductivity found in experiments can be easily understood, either by using the finite temperature approach, or by using an effective model in which the interband relaxation rate is temperature dependent. A large difference between transport coefficients in 2D and 3D Dirac systems is found. In 2D systems, there is a significant interband contribution to the effective number of charge carriers. In 3D systems, this component is negligible. The origin of this difference is in the additional factor k in dk in 3D integrals with respect to dk in 2D integrals.