Caustics have been known from prehistoric times as places where the intensity of light becomes extremely high, therefore the name meaning burning. The motion of a cold medium like cold dark matter qualitatively resembles the light rays and generically results in the focusing of the trajectories in extremely small volumes producing very high densities. This allows to make use of the concept of dark matter caustics in cosmology and astrophysics. Recently, the interest to caustics has been growing considerably. It is related to different suggestions to use the phenomenon of caustics for detection of mysterious dark matter through annihilation and gravitational lensing. I will review the current state of caustic studies.