This article is not a review in the conventional sense. Rather, it is a monographic study of the implications of detection in Al-Cu-Fe quasicrystals of the electronic heat capacity contributions associated with the two-level electron excitations. Our aim was to reveal correlations between these contributions, on the one hand, and specific features of electron transport, magnetic susceptibility, Hall-effect, tunnelling and optical spectra, on the other hand. It is shown that the full range of these features can be understood in the framework of the unified conceptual scheme based on two-level electron excitations.