(joint with Baldi and Ullmo) Given a polarizable variation of Hodge structures on a smooth quasi projective variety S, Cattani-Deligne-Kaplan proved that its Hodge locus (the locus of closed points of S where exceptional Hodge tensors do appear) is a countable union of closed algebraic subvarieties of S. In this talk I will discuss when this Hodge locus is actually algebraic.