Abstract: The radio-frequency (RF) ablation is a promising minimally invasive treatment for lesions in the human liver: A probe containing electrodes is placed in the tumor and connected to a generator. Consequently an electric current flows through the tissue and heats it up to temperatures of more than 60 degrees Celsius. This leads to a coagulation of the cell's proteins and thus a destruction of the malignant tissue. The success of the treatment heavily depends on a variety of patient-individual quantities, e.g. the local structure of the vascular system and material parameters like the water content of the tissue, its heat-capacity, its heat- and electric-conductivity, etc. So in the interest of the patient a thorough planning of the therapy must be made yielding an optimal position and orientation of the probe, and taking these important patient-specific properties into account. The talk focuses on various aspects of a numerical support for the planning of an RF-Ablation. A balance between the rigorous mathematical modeling and applicability in the clinical practice is shown. On the one hand the talk presents the modeling of RF ablation. This leads to a system of partial differential equations for the forward simulation as well as an optimal control problem for the RF-probe. On the other hand dimensional reductions of the mathematical model are presented, which are specifically tailored to support certain aspects of the therapy planning process for RF ablation. Finally challenges for the visualization and the communication of the results to the medical doctor are discussed.