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A survey on the recent work of Danciger, Gu\'eritaud and Kassel on Margulisspace-times and complete anti-de Sitter space-times. Margulis space-times arequotients of the 3-dimensional Minkowski space by (non-abelian) free groupsacting propertly discontinuously. Goldman, Labourie and Margulis have shownthat they are determined by a convex co-compact hyperbolic surface $S$ alongwith a first-order deformation of the metric which uniformly decreases thelengths of closed geodesics. Danciger, Gu\'eritaud and Kassel show that thosespace-times are principal $\mathbb R$-bundles over $S$ with time-like geodesicsas fibers, that they are homeomorphic to the interior of a handlebody, and thatthey admit a fundamental domain bounded by crooked planes. To obtain thoseresults they show that those Margulis space-times are "infinitesimal" versionsof 3-dimensional anti-de Sitter manifolds, and are lead to introduce a newparameterization of the space of deformations of a hyperbolic surface thatincrease the lengths of all closed geodesics.

Vari\'et\'es lorentziennes plates vues comme limites de vari\'et\'es anti-de Sitter, d'apr\`es Danciger, Gu\'eritaud et Kassel