Conservation laws with discontinuous flux functions arise in various models. In this talk we consider solutions to a class of conservation laws with discontinuous flux, where the flux function is discontinuous in both time and space, but regulated in the two variables. Convergence and the uniqueness of the vanishing viscosity limit for the viscous equation will be presented. For the case where a single discontinuity in the flux is present, the result is obtained by a backward Euler approximation and the Crandall-Ligget theory of nonlinear contractive semigroups. This is a joint work with Alberto Bressan and Graziano Guerra.