The aim of this paper is to study semantic notions of modularity in description logic (DL) terminologies and reasoning problems that are relevant for modularity. We define two notions of a module whose independence is formalised in a model-theoretic way. Focusing mainly on the DLs [Escr ][Lscr ] and [Ascr ][Lscr ][Cscr ], we then develop algorithms for module extraction, for checking whether a part of a terminology is a module, and for a number of related problems. We also analyse the complexity of these problems, which ranges from tractable to undecidable. Finally, we provide an experimental evaluation of our module extraction algorithms based on the large-scale terminology SNOMED CT.