How groups of individuals achieve coordination and collective action is an important topic in the natural sciences, but until recently the role of leadership in this process has been largely overlooked. In contrast, leadership is arguably one of the most important themes in the social sciences, permeating all aspects of human social affairs: the election of Barack Obama, the war in Iraq, and the collapse of the banks are all high-profile events that draw our attention to the fundamental role of leadership and followership. Converging ideas and developments in both the natural and social sciences suggest that leadership and followership share common properties across humans and other animals, pointing to ancient roots and evolutionary origins. Here, we draw upon key insights from the animal and human literature to lay the foundation for a new science of leadership inspired by an evolutionary perspective. Identifying the origins of human leadership and followership, as well as which aspects are shared with other animals and which are unique, offers ways of understanding, predicting, and improving leadership today.