  We present the recent result [8] concerning the existence of quasi-periodic
in time traveling waves for the 2d pure gravity water waves system in infinite
depth. We provide the first existence result of quasi-periodic water waves
solutions bifurcating from a completely resonant elliptic fixed point. The
proof is based on a Nash-Moser scheme, Birkhoff normal form methods and
pseudo-differential calculus techniques. We deal with the combined problems of
small divisors and the fully-nonlinear nature of the equations.
