The contemporary mathematical questions in X-ray tomography are often driven by practical challenges such as limited data, consider e.g. having a limited number of imaging angles or a limited field-of-view. There exists a number of proposed methods for image reconstruction given such incomplete data, however, much less is known about how to optimally design the imaging configuration if there are constraints on, e.g., to the radiation exposure, if individual projections do not cover all of the imaged object, or if there is a particular region of interest with exact location unknown. In this talk I discuss recent and ongoing work in Bayesian optimal experimental design related to X-ray tomography. This work is collaboration with Martin Burger, Andreas Hauptmann, Nuutti Hyvönen and Juha-Pekka Puska.