`Quasi‐mosaicity' is an effect of anisotropy in crystals that permits one to obtain a curvature of internal crystallographic planes that would be flat otherwise. The term `quasi‐mosaicity' was introduced by O. Sumbaev in 1957. The concept of `quasi‐mosaicity' was then retrieved about ten years ago and was applied to steering of charged‐particle beams at the Super Proton Synchrotron at CERN. Beams were deviated by exploiting channeling and volume reflection phenomena in curved crystals that show the `quasi‐mosaic' effect. More recently, a crystal of this kind was installed in the Large Hadron Collider at CERN for beam collimation by the UA9 collaboration. Since 2011, another important application involving the `quasi‐mosaic' effect has been the focalization of hard X‐rays and soft γ‐rays. In particular, the possibility of obtaining both high diffraction efficiency and the focalization of a diffracted beam has been proved, which cannot be obtained using traditional diffracting crystals. A comprehensive survey of the physical properties of `quasi‐mosaicity' is reported here. Finally, experimental demonstrations for adjustable values of the `quasi‐mosaic' curvature are provided.