Complexity science refers to the theoretical research perspectives and the formal modelling tools designed to study complex systems. A complex system consists of separate entities interacting following a set of (often simple) rules that collectively give rise to unexpected patterns featuring vastly different properties than the entities that produced them. In recent years a number of case studies have shown that such approaches have great potential for furthering our understanding of the past phenomena explored in Roman Studies. We argue complexity science and formal modelling have great potential for Roman Studies by offering four key advantages: (1) the ability to deal with emergent properties in complex Roman systems; (2) the means to formally specify theories about past Roman phenomena; (3) the power to test aspects of these theories as hypotheses using formal modelling approaches; and (4) the capacity to do all of this in a transparent, reproducible, and cumulative scientific framework. We present a ten-point manifesto that articulates arguments for the more common use in Roman Studies of perspectives, concepts and tools from the broader field of complexity science, which are complementary to empirical inductive approaches. There will be a need for constant constructive collaboration between Romanists with diverse fields of expertise in order to usefully embed complexity science and formal modelling in Roman Studies.