Why animal communication displays are so complex and how they have evolved are active foci of research with a long and rich history. Progress towards an evolutionary analysis of signal complexity, however, has been constrained by a lack of hypotheses to explain similarities and/or differences in signalling systems across taxa. To address this, we advocate incorporating a systems approach into studies of animal communication—an approach that includes comprehensive experimental designs and data collection in combination with the implementation of systems concepts and tools. A systems approach evaluates overall display architecture, including how components interact to alter function, and how function varies in different states of the system. We provide a brief overview of the current state of the field, including a focus on select studies that highlight the dynamic nature of animal signalling. We then introduce core concepts from systems biology (redundancy, degeneracy, pluripotentiality, and modularity) and discuss their relationships with system properties (e.g. robustness, flexibility, evolvability). We translate systems concepts into an animal communication framework and accentuate their utility through a case study. Finally, we demonstrate how consideration of the system-level organization of animal communication poses new practical research questions that will aid our understanding of how and why animal displays are so complex.