  This chapter gives an overview of the progress in the field of computational
superconductivity.
  Following the MgB2 discovery (2001), there has been an impressive
acceleration in the development of methods based on Density Functional Theory
to compute the critical temperature and other physical properties of actual
superconductors from first-principles. State-of-the-art ab-initio methods have
reached predictive accuracy for conventional (phonon-mediated) superconductors,
and substantial progress is being made also for unconventional superconductors.
The aim of this chapter is to give an overview of the existing computational
methods for superconductivity, and present selected examples of material
discoveries that exemplify the main advancements.
