Autism spectrum disorders (ASD) are complex neurodevelopmental disorders that are caused by genetic and/or environmental impacts, often probably by the interaction of both. They are characterised by deficits in social communication and interaction and by restricted and repetitive behaviours and interests from early childhood on, causing significant impairment. While it is clear that no animal model captures the full complexity of ASD in humans, genetic models are extremely useful for studying specific symptoms associated with ASD and the underlying cellular and molecular mechanisms. In this review we summarize the behavioral paradigms used in rodents to model ASD symptoms as they are listed in the DSM-5. We then review existing genetic rodent models with disruptions in ASD candidate genes, and we map their phenotypes onto these behavioural paradigms. The goal of this review is to give a comprehensive overview on how ASD symptoms can be studied in animal models and to give guidance for which animal models are appropriate to study specific symptom clusters.