The article describes theoretical work on the electron (exciton) mechanism of superconductivity in three-dimensional systems, which leads to high critical temperatures. Two models are considered: 1) systems with collective electrons of one group and localized electrons of another group (compounds of metals with dielectrics, organic substances, semiconductors or molecular crystals); 2) systems with two (or more) groups of collective electrons (metals with overlapping bands and multi-domain semiconductors). In the first case, uniform and granulated systems are considered. The effect of the critical fluctuations impeding the superconductivity is discussed in the case of granulated systems. Experimental work on the superconductivity of compounds of metals with dielectrics, organic substances, semiconductors and semimetals is described and discussed.