  Given a family of smooth complex projective varieties, the Hodge conjecture
predicts the algebraicity of the locus of Hodge classes. This was proven
unconditionnally by Cattani, Deligne and Kaplan in 1995. In a similar way,
conjectures on algebraic cycles have led Green and Griffiths to conjecture the
algebraicity of the zero locus of normal functions. This corresponds to a mixed
version of the theorem of Cattani, Deligne and Kaplan. This result has been
proven recently by Brosnan-Pearlstein, Kato-Nakayama-Usui, and Schnell building
on work of M. Saito. We will present some of the ideas around this theorem.
