The need for an ontological layer on top of data, associated with advanced reasoning mechanisms able to exploit the semantics encoded in ontologies, has been acknowledged both in the database and knowledge representation communities. We focus in this paper on the ontological query answering problem, which consists of querying data while taking ontological knowledge into account. To tackle this problem, we consider a logical framework based on existential rules, also called Tuple-Generating Dependencies or Datalog+/- rules. This framework can also be defined in graph terms. Query entailment with existential rules is not decidable, thus a crucial issue is to define decidable classes of rules as large as possible. This paper is a survey of decidable classes of rules, including a review of the main complexity results. It mostly relies on previous work presented at IJCAI'2009 [BLMS09] and KR'2010 [BLM10] (and developed in a journal paper [BLMS11]), updated to include very recent results.