  The basic features of multi-band superconductivity and its implications are
derived. In particular, it is shown that enhancements of the superconducting
transition temperature take place due to interband interactions. In addition,
isotope effects differ substantially from the typical BCS scheme as soon as
polaronic coupling effects are present. Special cases of the model are
polaronic coupling in one band as realized e.g., in cuprates, coexistence of a
flat band and a steep band like in MgB2, crossovers between extreme cases. The
advantages of the multiband approach as compared to the single band BCS model
are elucidated and its rather frequent realization in actual systems discussed
