Transcranial magnetic stimulation is a powerful technique that, by applying strong time-varying magnetic fields to the human head, induces electric fields in the brain that potentially influence brain activity. It is routinely used for diagnosis and treatment of brainrelated diseases. It is also an excellent research tool, as it can be used to non-invasively map causal relationships between different functional processes in the brain. In particular, one can influence (enhance or inhibit) the neural activity at one place of the cortex, and then observe the consequences elsewhere, as indexed by behavioral or physiological variables (readout). For this, we need to know where we stimulate and how exactly we influence the activity of neurons. This requires modeling efforts at the levels of electric fields and brain networks. In this presentation, I will first give an overview on the different levels of TMS modeling, comprising the prediction of the induced electric fields, the identification of the stimulation brain areas, the coupling between electric field and neural activity, and the dynamic response of neural networks. Then I will focus on the problem of mapping, that is, the identification of the anatomical localization of particular brain function. Although TMS features some degree of focality, the induced electric field still spans large parts of the cortex. Therefore, in order to localize exactly the neural populations underlying observable behavioral or physiological TMS effects, multiple stimulations with different coil positions/orientations are required. Common grid based mapping methods are time consuming and inaccurate. I will discuss a class of powerful new techniques that work with random coil configurations, accurate field modeling, and voxel-wise nonlinear regression. While these methods are easy to apply and perform very well with mapping muscle representations in the motor cortex, the application to more complex, cognitive brain processes requires further improvement. In particular, the ad-hoc or on-the-fly optimization of the stimulation parameters (coil positions/orientations) appears to be promising. Moreover, I will discuss how we might deal with the situation that readout variables depend on multiple, interconnected brain regions, which leads to a multi-modal regression problem. Finally, I will address the problem that all these techniques depend on models endowed with uncertain parameters. Sensitivity and uncertainty analysis based on generalized polynomial chaos (gPC) is shown to be an effective and extremely generic technique to verify the robustness of the methods and identify the most critical model parameters.