Description logics (DLs) are a family of logical formalisms that have initially been designed for the representation of conceptual knowledge in articial intelligence and are closely related to modal logics. In the last two decades, DLs have been successfully applied in a wide range of interesting application areas. In most of these applications, it is important to equip DLs with expressive means that allow to describe "concrete qualities" of real-world objects such as their weight, temperature, and spatial extension. The standard approach is to augment description logics with so-called concrete domains, which consist of a set (say, the rational numbers), and a set of n-ary predicates with a xed extension over this set. The "interface" between the DL and the concrete domain is then provided by a new logical constructor that has, to the best of our knowledge, no counterpart in modal logics. In this paper, we give an overview over description logics with concrete domains and summarize decidability and complexity results from the literature.