The paper provides a comprehensive overview of multilayer networks, which are essential for understanding complex systems that involve multiple types of relationships and interactions. The authors discuss the historical development of multilayer network theory, highlighting its origins in various disciplines such as sociology and engineering. They introduce a general framework for multilayer networks, which can accommodate multiple subsystems and layers of connectivity, and provide a dictionary of terminology to relate different concepts in the field. The paper reviews existing data sets that can be represented as multilayer networks and discusses methods for generalizing diagnostics from single-layer networks to multilayer networks. It also explores models of multilayer networks, methods for analyzing their properties, and dynamical processes on these networks. The authors conclude with a summary and an outlook on the future of multilayer network research.The paper provides a comprehensive overview of multilayer networks, which are essential for understanding complex systems that involve multiple types of relationships and interactions. The authors discuss the historical development of multilayer network theory, highlighting its origins in various disciplines such as sociology and engineering. They introduce a general framework for multilayer networks, which can accommodate multiple subsystems and layers of connectivity, and provide a dictionary of terminology to relate different concepts in the field. The paper reviews existing data sets that can be represented as multilayer networks and discusses methods for generalizing diagnostics from single-layer networks to multilayer networks. It also explores models of multilayer networks, methods for analyzing their properties, and dynamical processes on these networks. The authors conclude with a summary and an outlook on the future of multilayer network research.