In this Colloquium , the main features of the electron-lattice interaction are discussed and high values of the critical temperature up to room temperature could be provided. While the issue of the mechanism of superconductivity in the high T c cuprates continues to be controversial, one can state that there have been many experimental results demonstrating that the lattice makes a strong impact on the pairing of electrons. The polaronic nature of the carriers is also a manifestation of strong electronlattice interaction. One can propose an experiment that allows an unambiguous determination of the intermediate boson (phonon, magnon, exciton, etc.) which provides the pairing. The electron-lattice interaction increases for nanosystems, and this is due to an effective increase in the density of states.insulators. Doping leads to conductivity and then, for larger carrier concentration, to superconductivity. There is some characteristic value of the carrier concentration, n m , which corresponds to the maximum value of T c ≡ T c max . The underdoped (nn m ) regions are characterized by values of T c lower than T c max .Since the discovery of high T c oxides , there has been an intensive and fruitful study of these novel materials . However, despite intensive research, the question of the mechanism for these materials is still open.There has been growing evidence, mainly from various experimental studies, that the electron-lattice interaction is important for understanding the nature of high T c superconductivity in the cuprates. This interaction provides a direct contribution to the pairing of electrons, and also is clearly manifested in polaronic effects. The polaronic effects appear as a result of the strong electron-lattice interaction. In this case, a moving electron polarizes the lattice, and a shift in positions of neighboring ions forms a potential "box" for the electron. A polaron is a unit containing an electron that is moving with the lattice polarization caused by the electron itself (see,e.g., Ashcroft and Mermin,1976; Devresee, 2005, and see Sec.IV).This Colloquium is not a review, but rather a systematic description of our view, reflected in many publications on the subject. This Colloquium 9 also contains an extensive list of references that are related to this subject.Our viewpoint is that the electron-lattice interaction is an important ingredient of the current scenario and can explain superconductivity in novel systems including high temperature superconducting cuprates.The structure of the paper is as follows.The general properties of superconductivity caused by the electron-phonon interaction are discussed in Sec..II. Experimental data demonstrating the impact of this interaction are described in Sec.III. Section IV is concerned with the polaronic effect and the isotopic substitution. The phonon-plasmon mechanism for layered systems is described in Sec.V. Section VI contains a discussion of the electron-lattice interaction in the "pseudogap" state. A critical experiment...