This 70^th volume of the Bourbaki Seminar gathers the texts of the fifteen survey lectures delivered during the year 2017/2018. Among the topics addressed the reader will find the Zimmer program, Deligne-Lusztig varieties, cocompact-convex groups, Soergel bimodules, the Gan-Gross-Prasad conjectures, exponential sums, Bernoulli convolutions, the Navier-Stokes equations, the combinatorics of matroids, the dynamics of Schrödinger equations, the asymptotic distribution of Frobenius eigenvalues, stability conditions in birational geometry, the Monge-Ampère equation, harmonic maps in negative curvature, and the Fargues-Fontaine curves.