Distance geometry is a research area bridging mathematics and computer science with applicability to practical problems in a wide range of disciplines. In the majority of the applications, we are given an incomplete list of distances between pairs of objects, and we seek positions in Euclidean space realizing those distances. Classical applications include topics as protein conformation determination and sensor network localization, while emerging applications range from the study of molecular nanostructure to the adaptation of human movements in simulated environments. Distance geometry is also used in important data science applications such as compressed sensing, low rank matrix completion, and visualization of high-dimensional data.