In this talk we will present recent results about a sharp weighted weak type (1, 1) estimate for any Calder´on-Zygmund singular integral operator assuming that the weight satisfy the A1 condition. This result is related to a problem of Muckenhoupt-Wheeden that we will discuss. We will show that the endpoint result follows by proving first a corresponding sharp weighted Lp estimate both sharp on p and the A1 constant of the weight. We will end by showing the connection of this result with the A2 conjecture for Singular Integrals Operators. This is joint work with Andrei Lerner and Sheldy Ombrosi.