Animal communication is frequently multicomponent or multimodal, intermixing distinct signals of particular physical form into a complex display. Here we propose that adopting concepts from systems biology can advance comprehension of the function and evolution of animal signals. A systems approach to animal signaling considers the utility of a signal across all operational contexts (which could be ecological or behavioural), rather than limiting consideration to a single function for each signal.  It recognizes that signal elements can function differently across different ecological or behavioural contexts. We place a special emphasis on the concept of degeneracy, which has been pivotal in understanding several other evolved self-organizing systems but has thus far been overlooked in the animal signaling literature. A degenerate system (in contrast to a redundant system) contains structurally distinct elements that overlap in function in at least one context. Degenerate organization adds both robustness and adaptability to systems and could be a critical concept in guiding our understanding of the evolution of complexity in animal signaling. We suggest that incorporating key concepts from systems biology into animal communication will stimulate novel research questions and innovations towards an understanding of why animal signals are so complex, and how such signaling systems have evolved.