This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.We gratefully acknowledge the 806 supporters of MX16: the UC Davis Institute for Social Sciences, the U.S. Army Research Office 807 under Multidisciplinary University Research Initiative Award No. W911NF-13-1-0340, the UC 808 Davis Complexity Sciences Center, the UC Davis Anthropology Department, the UC Davis 809 Graduate Student Association, the UC Davis Department of Engineering, and the UC Davis 810 Office of Research.Network analysis has driven key developments in research on animal behaviour by providing quantitative methods to study the social structures of animal groups and populations. A recent formalism, known as multilayer network analysis, has advanced the study of multifaceted networked systems in many disciplines. It offers novel ways to study and quantify animal behaviour through connected ‘layers’ of interactions. In this article, we review common questions in animal behaviour that can be studied using a multilayer approach, and we link these questions to specific analyses. We outline the types of behavioural data and questions that may be suitable to study using multilayer network analysis. We detail several multilayer methods, which can provide new insights into questions about animal sociality at individual, group, population and evolutionary levels of organization. We give examples for how to implement multilayer methods to demonstrate how taking a multilayer approach can alter inferences about social structure and the positions of individuals within such a structure. Finally, we discuss caveats to undertaking multilayer network analysis in the study of animal social networks, and we call attention to methodological challenges for the application of these approaches. Our aim is to instigate the study of new questions about animal sociality using the new toolbox of multilayer network analysis.Natural Environment Research Council (NERC)National Science Foundation (NSF) Graduate Research FellowshipNFS IOS grantNIH R01NERC standard gran