Abstract--This paper summarizes results on a recently introduced family of Datalog-based languages, called Datalog+/-, which is a new framework for tractable ontology querying, and for a variety of other applications. Datalog+/- extends plain Datalog by features such as existentially quantified rule heads and, at the same time, restricts the rule syntax so as to achieve decidability and tractability. In particular, we discuss three paradigms ensuring decidability: chase termination, guardedness, and stickiness. Keywords-Knowledge Representation and Reasoning; Query Answering; Ontologies.