  This survey text deals with irrationality, and linear independence over the
rationals, of values at positive odd integers of Riemann zeta function. The
first section gives all known proofs (and connections between them) of
Ap\'ery's Theorem (1978) : $\zeta(3)$ is irrational. The second section is
devoted to a variant of the proof, published by Rivoal and Ball-Rivoal, that
infinitely many $\zeta(2n+1)$ are irrational. The end of this text deals with
more quantitative statements.
