The crucial feature of neuronal ensembles is their high complexity and variability. This makes modelling and computation very difficult, in particular for detailed models based on first principles. The problem starts with modelling geometry, which has to extract the essential features from those highly complex and variable phenotypes and at the same time has to take in to account the stochastic variability. Moreover, models of the highly complex processes which are living on these geometries are far from being well established, since those are highly complex too and couple on a hierarchy of scales in space and time. Simulating such systems always puts the whole approach to test, including modeling, numerical methods and software implementations. In combination with validation based on experimental data, all components have to be enhanced to reach a reliable solving strategy. To handle problems of this complexity, new mathematical methods and software tools are required. In recent years, new approaches such as parallel adaptive multigrid methods and corresponding software tools have been developed allowing to treat problems of huge complexity. In the lecture we present a study on infoldings of neuron nuclei. Using first-principle based modelling, we were able to describe the effect of invaginations in neuron nuclei. We will further give a three dimensional model for the simulation of signal processing in neurons. Part of this approach is a method to reconstruct the geometric structure of neurons from data measured by 2-photon microscopy. We then present the 3d cable equations as a fully resolved model for computing the signal transduction in neurons. The model includes ephaptic couplings.