High-T-c and unconventional superconductivity appears in a number of different materials with different physical properties. A common characteristics shared by almost all these compounds is that they are 'bad metal' in the sense that their effective charge carrier density is quite small, leading to a small Fermi energy E-F. In such a situation the dynamics of the electronic and lattice degrees of freedom becomes comparable (omega(ph) similar to E-F) driving these systems towards a breakdown of the Born-Oppenheimer adiabatic principle (omega(ph) << E-F) ruled by the comparison between the phonon frequency scale omega(ph) and E-F. The standard concept of Fermi liquid picture applied to the electron-phonon interaction needs thus to be deeply revised. We discuss the interesting implications of the onset of nonadiabatic effects on many properties of systems with small Fermi energy. (c) 2005 Elsevier Ltd. All rights reserved.