Radiofrequency (RF) ablation is a minimally invasive therapy form for the treatment of tumors in the human liver. A needle-shaped applicator is percutaneously inserted into the tumor and induces heat via an electric current flow, by this destroying the tumor thermally. The talk presents the essentials of a mathematical model and numerical simulation of RF ablation, in their current state-of-the-art of the author's work. In particular, the effect of evaporation of cell water is addressed, which complicates the model substantially. Different approaches to deal with this situation are presented. Also, the talk will introduce a technique to speed-up the patient-individual prediction by the use of look-up tables. Finally, aspects of future research on this topic will be identified.