Large random matrices were born about a century ago in the work of the statistician Wishart to analyze big array of noisy datas. It was then shown in the fifties by Wigner and Dyson  to model well the Hamiltonian of certain heavy nuclei, hence finding its way in quantum physics. Even more surprisingly, Montgomery gave a numerical evidence that random matrices are intimately related to the zeroes of Riemann Zeta function in the seventies. But it is really only after the birth of MSRI that random matrix theory developed as a mature field. In this talk, after underlying a few other fields where random matrices play a central role, I will discuss the random matrix theory of Bernoulli  Matrices, old and new.

Estimating the probability of rare events, namely large deviations principle, for the spectrum of Wigner matrices with compactly supported entries is a challenge. In this talk we will discuss how the asymptotics of Spherical integrals can be derived and used to study such problems. This is based on  recent joint works with Augeri, Belinschi, Huang and Husson.

We will discuss transport maps techniques to construct isomorphisms of C^* algebras and study the local fluctuations of the eigenvalues of polynomials in several GUE matrices.