The further development of Peyve’s concept of deep faults in the Earth’s crust and brittle part of the lithosphere is discussed. Three aspects are accentuated in this paper: (1) the modern definition of the term deep fault; (2) the parameters of deep faults as ruptures of the geological medium and three-dimensional, often boundary, geological bodies; and (3) reactivation of deep faults, including the development of this process in real time. Peyve’s idea of deep faults readily fitted into the concept of new global tectonics (plate tectonics). This was facilitated, first of all, by the extensive efforts made to elaborate Peyve’s ideas by a large group of researchers at the Geological Institute of the Russian Academy of Sciences (GIN RAS) and other scientists. At present, the term deep fault has been extended and transformed to cover three-dimensional geological bodies; the geological and geophysical properties and parameters of these bodies, as well as their reactivation (recurrent activation) in real time, have been studied.