An important issue that arises when querying description logic (DL) knowledge bases is how to handle the case in which the knowledge base is inconsistent. Indeed, while it may be reasonable to assume that the TBox (ontology) has been properly debugged, the ABox (data) will typically be very large and subject to frequent modifications, both of which make errors likely. As standard DL semantics is useless in such circumstances (everything is entailed from a contradiction), several alternative inconsistency-tolerant semantics have been proposed with the aim of providing meaningful answers to queries in the presence of such data inconsistencies. In the first part of this chapter, we present and compare these inconsistency-tolerant semantics, which can be applied to any DL (or ontology language). The second half of the chapter summarizes what is known about the computational properties of these semantics and gives an overview of the main algorithmic techniques and existing systems, focusing on DLs of the DL-Lite family.