Answering queries while taking an ontology into account has been studied over the last fifteen years to ease data integration. The goal is to allow users to express their queries in a vocabulary they are familiar with, while facilitating data integration and providing more complete sets of answers thanks to the exploitation of the semantics of the query terms. Decidability, complexity and algorithms developed so far have focused on the case where Boolean conjunctive queries are used to query a so-called knowledge base. In this manuscript, we explore the limitations of this setting, and suggest a few extensions that are relevant from an applicative point of view. Expressivity is studied through the prism of descriptive complexity, while the proposed extensions escape from the Boolean conjunctive query framework, by either allowing path queries, or by going beyond the Boolean case, by supporting counting features or providing meta-data about theprovenance of an answer.