Appropriate and efficient representations of domains, objects, and scenes are an important issue in the fields of geometric modelling, numerical simulation, and visualization. Though various techniques have been developed and are successfully used as single-purpose solutions, there is still some lack of comprehensive approaches that allow to base modelling, simulation, and visualization on the same representation of the underlying geometry or that offer, at least, efficient interfaces between the different descriptions. In this paper, we want to discuss how hierarchical schemes can close this gap and, thus, allow a straightforward embedding of numerical simulations into a more general context.