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