There is a growing understanding that transport properties of complex oxides and individual molecules are dominated by polaron physics. In superconducting oxides the long-range Froehlich and short-range Jahn-Teller electron-phonon interactions bind carriers into real space pairs - small bipolarons with surprisingly low mass but sufficient binding energy, while the long-range Coulomb repulsion keeps bipolarons apart preventing their clustering. The bipolaron theory numerically explains high Tc values without any fitting parameters and describes other key features of the cuprates. The same approach provides a new insite into the theory of transport through molecular nanowires and quantum dots (MQD). Attractive polaron-polaron correlations lead to a "switching" phenomenon in the current-voltage characteristics of MQD. The degenerate MQD with strong electron-vibron coupling has two stable current states (a volatile memory), which might be useful in molecular electronics.