Electrical impedance tomography is a non-invasive method for imaging the electrical conductivity of an object from voltage measurements on its surface. This inverse problem suffers threefold: it is highly nonlinear, severely ill-posed, and highly under-determined. To obtain yet reasonable reconstructions, maximal information needs to be extracted from the data. We will present and analyze a holistic Newton-type method which addresses all these challenges. Finally, we demonstrate the performance of this concept numerically for simulated and measured data.