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 definition and PTV margins have improved through the development of novel imaging techniques and better image guidance, respectively. CTV definition is sometimes considered the weakest element in the planning process. CTV definition is particularly complex since the extension of microscopic disease cannot be seen using currently available in-vivo imaging techniques. Instead, CTV definition has to incorporate knowledge of the patterns of tumor progression. While CTV delineation has largely been considered the domain of radiation oncologists, this paper, arising from a 2019 ESTRO Physics research workshop, discusses the contributions that medical physics and computer science can make by developing computational methods to support CTV definition. First, we overview the role of image segmentation algorithms, which may in part automate CTV delineation through segmentation of lymph node stations or normal tissues representing anatomical boundaries of microscopic tumor progression. The recent success of deep convolutional neural networks has also enabled learning entire CTV delineations from examples. Second, we discuss the use of mathematical models of tumor progression for CTV definition, using as example the application of glioma growth models to facilitate GTV-to-CTV expansion for glioblastoma that is consistent with neuroanatomy. We further consider statistical machine learning models to quantify lymphatic metastatic progression of tumors, which may eventually improve elective CTV definition. Lastly, we discuss approaches to incorporate uncertainty in CTV definition into treatment plan optimization as well as general limitations of the CTV concept in the case of infiltrating tumors without natural boundaries.