The Classic Maya represent a newly important topic for political anthropology and the study of pre-Modern societies. The decipherment of their script offers a trove of primary sources that allow us, uniquely in the ancient Americas, to compare and contrast a rich material record with a significant historical one. Whether our goal is to comprehend social power in its broadest sense, or to understand the nature of specific institutions such as monarchy, complex societies isolated from the cross-fertilisations of the Old World have clear comparative value. As such, what we can learn about the Maya casts useful light on universal themes and will be of wider relevance to the field.