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

Progr\`es r\'ecents sur les fonctions normales (d'apr\`es Green-Griffiths, Brosnan-Pearlstein, M. Saito, Schnell...)