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We argue that the extension of the BCS theory to the strong-coupling regime describes the high-temperature superconductivity of cuprates and the colossal magnetoresistance (CMR) of ferromagnetic oxides if the phonon dressing of carriers and strong attractive correlations are taken into account. The attraction between carriers, which is prerequisite to high-temperature superconductivity, is caused by an almost unretarted electron-phonon interaction sufficient to overcome the direct Coulomb repulsion in the strong-coupling limit, where electrons become polarons and bipolarons (real-space electron or hole pairs dressed by phonons). The long-range Froehlich electron-phonon interaction has been identified as the most essential in cuprates providing "superlight" lattice polarons and bipolarons. A number of key observations have been predicted and/or explained with polarons and bipolarons including unusual isotope effects, normal state (pseudo)gaps, upper critical fields, etc. Here some kinetic, magnetic, and more recent thermomagnetic normal state measurements are interpreted in the framework of the strong-coupling theory, including the Nernst effect and normal state diamagnetism. Remarkably, a similar strong-coupling approach offers a simple explanation of CMR in ferromagnetic oxides, while the conventional double-exchange (DEX) model, proposed half a century ago and generalised more recently to include the electronphonon interaction, is in conflict with a number of modern experiments. Among these experiments are site-selective spectroscopies, which have shown that oxygen p-holes are current carriers rather than d-electrons in ferromagnetic manganites (and in cuprates) ruling out DEX mechanism of CMR. Also some samples of ferromagnetic manganites manifest an insulating-like optical conductivity at all temperatures contradicting the DEX notion that their ferromagnetic phase is metallic. On the other hand, the pairing of oxygen holes into heavy bipolarons in the paramagnetic phase and their magnetic pair-breaking in the ferromagnetic phase account for the first-order ferromagnetic phase transition, CMR, isotope effects, and pseudogaps in doped manganites. Here we propose an explanation of the phase coexistence and describe the shape of resistivity of manganites near the transition in the framework of the strong-coupling approach.
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