We study the data complexity of instance checking and conjunctive query answering in the
family of description logics, with a particular emphasis on the boundary of tractability. We identify a large number of intractable extensions of
, but also show that in
, the extension of
with inverse roles and global functionality, conjunctive query answering is tractable regarding data complexity. In contrast, already instance checking in
extended with only inverse roles or global functionality is
-complete regarding combined complexity.