The standard family (or Taylor-Chirikov standard family) is an example of a family of dynamical systems having simple expressions but with complicated dynamics. A famous conjecture of Sinai is that for large parameter the standard map has positive entropy for the Lebesgue measure. In this seminar, I will talk about a recent result which I obtain the uniqueness of the measure of maximal entropy of the standard map for sufficiently large parameters. Moreover, I obtain that such a measure is Bernoulli and the periodic points whose Lyapunov exponents are bounded away from zero equidistribute with respect to this measure. I can also obtain estimates on the Hausdorff dimension of the measure and of the support.