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 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. We also mention some yet open questions. 
I.I. Mazin and V.P. Antropov