We study learning of description logic TBoxes in Angluin et al.’s framework of exact learning via queries. We admit entailment queries (“is a given subsumption entailed by the target TBox?”) and equivalence queries (“is a given TBox equivalent to the target TBox?”), assuming that the signature and logic of the target TBox are known. We present three main results: (1) TBoxes formulated in DL-Lite with role inclusions and composite concepts on the right-hand side of concept inclusions can be learned in polynomial time; (2) EL TBoxes with only concept names on the right-hand side of concept inclusions can be learned in polynomial time; and (3) EL TBoxes cannot be learned in polynomial time. It follows that non-polynomial time learnability of EL TBoxes is caused by the interaction between existential restrictions on the right and left-hand sides of concept inclusions. We also show that neither entailment nor equivalence queries alone are sufficient in cases (1) and (2) above.