Assessing the tumor response of liver cancer lesions after intraarterial therapies is of major clinical interest. Over the last two decades, tumor response criteria have come a long way from purely size-based, anatomic methods such as the Response Evaluation Criteria in Solid Tumors towards more functional, enhancement- and diffusion-based parameters with a strong emphasis on MRI as the ultimate imaging modality. However, the relatively low reproducibility of those one- and 2D techniques (modified Response Evaluation Criteria in Solid Tumors and the European Association for the Study of the Liver criteria) provided the rationale for the development of new, 3D quantitative assessment techniques. This review will summarize and compare the existing methodologies used for 3D quantitative tumor analysis and provide an overview of the published clinical evidence for the benefits of 3D quantitative tumor response assessment techniques.