  This survey article is the written version of a talk given at the Bourbaki
seminar in April 2021. We give an introduction to Zagier's conjecture on
special values of Dedekind zeta functions, and its relation to $K$-theory of
fields and the theory of motives. We survey recent progress on the conjecture
and in particular the proof of the $n=4$ case of the conjecture by Goncharov
and Rudenko.
