In more than half a century of intensive and extensive development the Jahn-Teller effect (JTE) rose from a specific feature of polyatomic systems in degenerate electronic states to a general tool of structural problem-solving applicable to any molecular and solid state system [1]. This became clear after it was proved that the pseudo JTE (PJTE) is the only source of instability and spontaneous symmetry breaking (SSB) of high-symmetry configurations of polyatomic systems in nondegenerate states (see in [2]). Together, the JTE and PJTE are the only source of SSB in matter. In the plenary talk a general introduction plus our latest novel findings in application of the JTE and PJTE are presented. The main topics included are: (1) Hidden JTE and PJTE. There are many cases when the molecular system is distorted in the equilibrium configuration, but at first sight there is neither electronic degeneracy nor pseudodegeneracy. We have shown that in these cases the SSB is still due to the JTE and/or the PJTE that are hidden in the excited states. In application to the ozone molecule (hidden JTE [3]), CO3, A4B4, A=C, Si, B=H, F, and CuF3 (hidden PJTE [4]), specific structural features and novel molecular properties are revealed with potential interesting applications [5]. (2) Unexpected SSB in linear molecules. For the B—N—B (ground state) and Cl—Cu— Cl (excited state) molecules the PJTE predicts a non-centro-symmetrical linear configuration in equilibrium which is confirmed by ab initio calculations [6]. We have shown that in linear molecules the Renner-Teller effect just splits the degenerate term, but does not produce bending instability; the latter is due to the PJTE only [7]. Quite recently a novel type of SSB has been revealed: in linear triatomics the PJTE induced bending is angular dependent [8]. (3) Rich varieties of structural configurations predicted by the JTE and PJTE, illustrated by a small, but representative molecule C3H3 [9]. (4) Local origin of dipolar instability in crystals triggering ferroelectric phase transitions in crystals [10] and explaining the dependence of multiferroic properties on the electronic configuration of the transition metal [11].