We report on a recently introduced family of expressive extensions of Datalog, called Datalog<sup>±</sup>, which is a new framework for representing ontological axioms in form of integrity constraints, and for query answering under such constraints. Datalog± is derived from Datalog by allowing existentially quantified variables in rule heads, and by enforcing suitable properties in rule bodies, to ensure decidable and efficient query answering. We first present different languages in the Datalog± family, providing tight complexity bounds for all cases but one (where we have a low complexity AC<sub>0</sub> upper bound). We then show that such languages are general enough to capture the most common tractable ontology languages. In particular, we show that the <i>DL-Lite</i> family of description logics and <i>F-Logic Lite</i> are expressible in Datalog±. We finally show how stratified negation can be added to Datalog± while keeping ontology querying tractable in the data complexity. Datalog± is a natural and very general framework that can be successfully employed in different contexts such as data integration and exchange. This survey mainly summarizes two recent papers.