Inverse problems are at the heart of data science. The field is cross-­disciplinary both within mathematics, encompassing aspects of pure, applied as well as statistics, and across subjects, including physical sciences, engineering, medicine and biology. Inverse problems arise in almost all fields of science when details of a postulated model have to be determined from a set of observed data. With inverse problems, scientists observe an effect and work to determine the cause; the ultimate goal is to find essential information (an object or material properties) that is hidden within the measurements. Biomedical imaging, for instance, gives rise to a variety of inverse problems in which the common goal is to produce an image visualising the interior of a living organism.