  We study inverse problems of reconstructing static and dynamic discrete
structures from tomographic data (with a special focus on the `classical' task
of reconstructing finite point sets in $\mathbb{R}^d$). The main emphasis is on
recent mathematical developments and new applications, which emerge in
scientific areas such as physics and materials science, but also in inner
mathematical fields such as number theory, optimization, and imaging. Along
with a concise introduction to the field of discrete tomography, we give
pointers to related aspects of computerized tomography in order to contrast the
worlds of continuous and discrete inverse problems.
