In 2011, the physicist will celebrate the 100th anniversary of the discovery of superconductivity by H.K. Onnes[1]; after one hundred years, this is still one of the most vital fields of condensed matter physics, which continues to bring new surprises.The research of this field is extremely intense, not only because superconductors have many possible applications - energy transmission and storage, electronic devices such as SQUID - but also because they posed fundamental theoretical questions, which have lead to the of many new theoretical methods.In the last ten years, there have been several breakthroughs on the experimental side: the report of superconductivity in magnesium diboride (MgB2)[2], which, after more than 40 years, has “broken” the theoretical limit to the critical temperatures of phonon-based superconductors (2001).The report of superconductivity in boron-doped diamond[3] (2004), which has opened a new field of research in superconducting semiconductors and, finally, the report of superconductivity in iron-based superconductors (FeBSC)[4], which are probably the first clear example of compounds, where superconductivity is unambiguously mediated by magnetic fluctuations (2008). In parallel, on the theoretical side, a new, multidisciplinary approach to the problem, combining “traditional” first-principles calculations with model many-body approaches has emerged. This Computational superconductivity has seen a rapid development in the last few years, starting with the explanation of two-gap superconductivity in MgB2 and other graphite-like compounds, the development of Density-Functional Theory of the superconducting state, and, more recently, the prediction of unconventional superconductivity in Fe-based compounds (2008)