The author gives an overview of a theory of continuous dependence and error estimation for the entropy solution of scalar hyperbolic conservation laws. They lead to a complete \(l^{\infty} (l^1)\)-approximation theory with which error estimates for numerical methods for this type of equation can be obtained. The approach he considers consists in obtaining continuous dependence results for the solutions of parabolic conservation law and deducing from them the corresponding results for the entropy solution.