Electronic structure, electron-phonon coupling, and multiband effects in MgB2

We review the current situation in the theory of superconducting and transport properties of MgB2. First principle calculations of the electronic structure and electron-phonon coupling are discussed and compared with the experiment. We also present a brief description of the multiband effects in superconductivity and transport, and how these manifest themselves in MgB2. (C) 2002 Elsevier Science B.V. All rights reserved.