A review is presented of the observational data on detection of cosmic $\gamma$ rays. The importance of observations in $\gamma$ astronomy in solution of a number of basic problems of cosmic-ray physics, astrophysics, and cosmology (for example, the origin and sources of cosmic rays) is emphasized. Observations of isotropic diffuse and galactic components of $\gamma$ radiation are presented and analyzed. Methods are discussed for searching for discrete sources of cosmic $\gamma$ rays, and results are presented on detection of $\gamma$-ray fluxes from the sun, the Crab nebula, pulsar NP 0532, Cyg X-3, and other discrete sources. The results of the observations definitely indicate a variability of the discrete $\gamma$-ray sources. In conclusion a short review is given of new methods of $\gamma$-astronomy observations.