The recently discovered anisotropic superconductor MgB2 is the first of its kind showing the intriguing properties of two-band superconductivity. By tunneling experiments using thin film tunnel junctions, electron-coupled phonon spectra were determined showing that superconductivity in MgB2 is phonon mediated. In a further analysis, which involves first principles calculations, the strongest feature in these spectra could be traced back to the key quantity of two-band superconductivity, the interband pairing interaction. For the phonons, this interaction turns out quite selective. It involves mainly low-energy optical phonon modes, where the boron atoms move perpendicular to the boron planes.