Treatment planning in radiotherapy distinguishes three target volume concepts: the gross tumor volume(GTV), the clinical target volume (CTV), and the planning target volume (PTV). Over time, GTV definitionand PTV margins have improved through the development of novel imaging techniques and better imageguidance, respectively. CTV definition is sometimes considered the weakest element in the planning pro-cess. CTV definition is particularly complex since the extension of microscopic disease cannot be seenusing currently available in-vivo imaging techniques. Instead, CTV definition has to incorporate knowl-edge of the patterns of tumor progression. While CTV delineation has largely been considered the domainof radiation oncologists, this paper, arising from a 2019 ESTRO Physics research workshop, discusses thecontributions that medical physics and computer science can make by developing computational meth-ods to support CTV definition. First, we overview the role of image segmentation algorithms, which mayin part automate CTV delineation through segmentation of lymph node stations or normal tissues repre-senting anatomical boundaries of microscopic tumor progression. The recent success of deep convolu-tional neural networks has also enabled learning entire CTV delineations from examples. Second, wediscuss the use of mathematical models of tumor progression for CTV definition, using as example theapplication of glioma growth models to facilitate GTV-to-CTV expansion for glioblastoma that is consis-tent with neuroanatomy. We further consider statistical machine learning models to quantify lymphaticmetastatic progression of tumors, which may eventually improve elective CTV definition. Lastly, we dis-cuss approaches to incorporate uncertainty in CTV definition into treatment plan optimization as well asgeneral limitations of the CTV concept in the case of infiltrating tumors without natural boundaries.