We present some recent results on the problem of approximating a scalar conservation law by a conservation law with nonlocal flux. As convolution kernel in the nonlocal flux, we consider an exponential-type approximation of the Dirac distribution. We prove that the (unique) weak solution of the nonlocal problem converges strongly in $C(L^1_{loc})$ to the entropy solution of the local conservation law. This talk is based on joint works with G. M. Coclite, J.-M. Coron, A. Keimer, and L. Pflug.