Many interesting infinite dimensional Lie (super conformal) algebras can be thought as being “finite dimensional” when viewed, not as algebras over the given base field, but rather as algebras over their centroids (usually a Laurent polynomial ring). From this point of view, the algebras in question look like “twisted forms" of simpler objects which with one is familiar. The quintessential example of this type of behaviour is given by the affine Kac-Moody Lie algebras. Once the twisted form point of view is embraced, the theory of torsors and reductive group schemes developed by Demazure and Grothendieck [SGA3] arises naturally. The talk will explain these concepts and connections.