In a generalization of the latest achievements in this field, and as a pattern of massive applications, we present here the Jahn-Teller effect (JTE) and pseudo-JTE (PJTE) as general tools in the study of physical and chemical phenomena related to structural properties of polyatomic systems. We show that the JTE and PJTE are no more specific features of particular (rare) systems (as it was assumed earlier), but virtual properties of all molecular and solid state formations. They occur as a result of vibronic coupling that compensates for the error (inadequacy) introduced in semi-classical definitions of polyatomic configurations by their high-symmetry nuclear positions, thus appending the basic understanding of related phenomena with a new dimension. The implications of the JTE and PJTE in observable properties varies significantly, being especially strong in the states of electronic degeneracy or pseudodegeneracy, but they cannot be a priory fully excluded for any system. After the introductory sections we demonstrate some of the more recent results of the influence of these effects on the observables in physical and chemical phenomena, together with a wide range of applications. The latter are conventionally separated in three parts: intermediate states in chemical and photochemical reactions, manipulation of structural properties of polyatomic systems targeting the JTE and PJTE, and applications in materials science. The illustrative examples include the origin of sudden polarization in photochemical reactions, methods of planarization of puckered (buckled) two-dimensional systems, modification of crystal sublattices by targeting the JTE parameters, the defining role of JTE and PJTE in electronics and spintronics, the origin of ferroelectricity and multiferroicity, as well as a novel property of solids, orientational polarization, and its applications.