Percutaneous, image-guided thermal tumor ablation procedures are used increasingly for minimally invasive, local treatment of tumors in the liver. The planning of these procedures; the support of targeting, monitoring, and controlling during the intervention itself; and the assessment of the treatment response can all benefit significantly from computer assistance. The outcome can be optimized by supporting the physician in the process of determining an intervention strategy that enables complete destruction of the targeted tumor while reducing the danger of complications. During the intervention, computer-assisted methods can be used to guide the physician in the implementation of the intended strategy by providing planning information. Assessment of the intervention result is carried out by comparison of the achieved coagulation with the target tumor volume. Supporting this comparison facilitates the early detection of potential recurrences. This report provides an overview of state-of-the-art computer-assisted methods for the support of thermal tumor ablations in the liver. Proper approaches for image segmentation, access-path determination, simulation, visualization, interventional guidance, and post-interventional assessment, as well as integrated work flow-oriented solutions, are reviewed with respect to technical aspects and applicability in the clinical setting.