This report documents the program and the outcomes of Dagstuhl Seminar 18442, "Visualization and Processing of Anisotropy in Imaging, Geometry, and Astronomy", which was attended by 30 international researchers, both junior and senior. Directional preferences or anisotropies are encountered across many different disciplines and spatial scales. These disciplines share a need for modeling, processing, and visualizing anisotropic quantities, which poses interesting challenges to applied computer science. With the goal of identifying open problems, making practitioners aware of existing solutions, and discovering synergies between different applications in which anisotropy arises, this seminar brought together researchers working on different aspects of computer science with experts from neuroimaging and astronomy. This report gathers abstracts of the talks held by the participants, as well as an account of topics raised within the breakout sessions.