The use of ontologies is now prevalent in a large number of domains.  In the last decade, the standardisation of the OWL family of languages has led to the widespread use of Description Logics to define ontologies.  At the same time, the computational properties of Description Logics have been extensively studied.  However, much less attention has been given to the cognitive complexity arising from ontologies, and in particular to the cognitive difficulties experienced in understanding and using certain Description Logic features.  This talk will report on a survey of ontology users, and discuss some of their difficulties, including those arising from the use of Description Logics.  A challenge now is to use cognitive science to understand the difficulties experienced in using Description Logics, and the talk will go on to discuss some potentially relevant theories from cognitive science and how they might be applied.