We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit. Technically, the heart of the argument are new laws of large numbers at the exponential scale, proved through an explicit combinatorics approach. Our result only requires weak regularity on the interaction kernel in negative Sobolev spaces, thus including the Biot-Savart law and the point vortices dynamics for the 2d incompressible Navier-Stokes. For dissipative gradient flows, we may allow any singularity lower than the Poisson kernel. This talk corresponds to a joint work with Z. Wang and an upcoming work with D. Bresch and Z. Wang.