The volume 1/f noise in GaAs, Si and 6H-SiC appears as a result of fluctuations of the occupancy of those levels that form the density-of-state tails near the band edges. Tails of this kind are due to the presence of imperfections (defects, local stresses, impurities, clusters, etc.) and exist in any real crystal. A model of the volume 1/f noise in semiconductors is put forward. The model predicts the existence of several physical effects associated with the same density-of-state tails near the band edge which are responsible for the volume 1/f noise. These effects are: a nonmonotonic dependence of the 1/f noise on the intensity of the band-to-band illumination (minority carrier concentration), a specific mechanism of a persistent photoconductivity, an increase of the 1/f noise intensity with deteriorating of the structural perfection of a semiconductor. All these effects have been observed experimentally in GaAs and Si.