Résumé
This survey article is the written version of two talks given at the
Journées X-UPS 2019 "Périodes et transcendance" at École polytechnique.
We give a gentle introduction to the study of multiple zeta values, from
Euler's solution to the Basel problem to modern Galois theoretic tools. We
emphasize the role of the theory of motives which conjecturally controls the
structure of the algebra of multiple zeta values.