Computational Inverse Problems are all about the application. The driving question is how to extend the thorough theory of an Inverse Problem to an algorithm, which can be implemented and ultimately produces a reconstruction of the unknown object. Furthermore, if one deals with real life measurements or even just simulations on a computer, the discretization to a finite dimensional setting is an important issue. In particular, how does the problem at hand behave if we have only finite, possibly noisy, data available?