Possible manifestations of new physics in rare (exotic) decays of orthopositronium (o - Ps) are briefly reviewed. It is pointed out that models with infinite additional dimension(s) of Randall-Sundrum type predict disappearance of orthopositronium into additional dimension(s). The experimental signature of this effect is the invisible decay of orthopositronium. We point out that this process may occur at a rate within two or three orders of magnitude of the present experimental upper limit. We also propose a model with a light weakly interacting boson leading to o - Ps --> invisible decays at the experimentally interesting rate. We discuss this in details and stress that the existence of invisible decay of orthopositronium in vacuum could explain the o - Ps decay rate puzzle. Thus, our result enhances the existing motivation and justifies efforts for a more sensitive search for o - Ps --> invisible decay in a near future experiment.