Newton-type concepts are well-known to constitute an efficient tool for non-linear problems which are sufficiently regular. In many problems of practical importance such regularity properties are not satisfied. In this talk it is shown how semi-smooth techniques, which lead to superlinearly convergent algorithms, can be applied to problems which are Newton-differentiable but not necessarily C^1 at the solution. Such problems arise in a multitude of applications including optimal control of variational inequalities, portfolio optimization, image processing based on BV and L^1 type functionals, and in optimal control of parital differential equations.