Two current algebra functors were introduced by Alekseev and Severa: they assign Lie algebras to a pair consisting of a smooth manifold $M$ and a differential graded Lie algebra $A$. Important extensions of current algebras can be obtained via those current algebra functors: all central extensions by the fundamental current algebra cocycles (including affine Lie algebras on the circle), the Fadeev-Mickelsson-Sahtashvili abelian extension, and the Lie algebra of symmetries for the sigma model. Finally we present groups integrating Lie algebras obtained via current algebra functors.