Villani va estudiar en la École normale supérieure entre 1992 i 1996, on va treballar com a assistent de càtedra. Va rebre el seu doctorat a la Universitat París-Dauphine el 1998, sota la supervisió de Pierre-Louis Lions, i va ingressar com a professor en l'Escola Normal Superior de Lió el 2000. Actualment és professor de la Universitat de Lió i de 2009 a 2017 és director de l'Institut Henri Poincaré, a París.[1][2]
A Review of Mathematical Topics in Collisional Kinetic Theory, in Handbook of Mathematical Fluid Dynamics, edited by S. Friedlander and D. Serre, vol. 1, Elsevier, 2002, ISBN 978-0-444-50330-5 .
Topics in Optimal Transportation, volume 58 of Graduate studies in mathematics, American Mathematical Society, 2003, ISBN 978-0-8218-3312-4.
Optimal transportation, dissipative PDE's and functional inequalities, pp. 53–89 in Optimal Transportation and Applications, edited by L. A. Caffarelli and S. Salsa, volume 1813 of Lecture Notes in Mathematics, Springer, 2003, ISBN 978-3-540-40192-6.
Cercignani's conjecture is sometimes true and always almost true, Communications in Mathematical Physics, vol. 234, No. 3 (March 2003), pp. 455–490.
On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation (with Laurent Desvillettes), Inventiones Mathematicae, vol. 159, #2 (2005), pp. 245–316.
Mathematics of Granular Materials, Journal of Statistical Physics, vol. 124, #2–4 (July/August 2006), pp. 781–822.
Optimal transport, old and new, volume 338 of Grundlehren der mathematischen Wissenschaften, Springer, 2009, ISBN 978-3-540-71049-3.
O'Connor, John J.; Robertson, Edmund F. «Cédric Villani» (en anglès). MacTutor History of Mathematics archive. School of Mathematics and Statistics, University of St Andrews, Scotland.