Finding solutions to the entangled problems of human population growth, resource exploitation, ecosystem degradation, and biodiversity loss is considered humanity's grand challenge. Small and isolated societies of the past, such as the Rapanui of Easter Island, constitute ideal laboratories for understanding the consequences of human-driven environmental degradation and associated crises. By integrating different processes into a coherent and quantitative framework, mathematical models can be effective tools for investigating the ecological and socioeconomic history of these ancient civilizations. Most models of Easter Island are grounded around the Malthusian theory of population growth and designed as Lotka-Volterra predator-prey systems. Within ranges of plausible parameter values, these dynamic systems models predict a population overshoot and collapse sequence, in line with the ecocidal view about the Rapanui. With new archaeological evidence coming to light, casting doubts on the classical narrative of a human-induced collapse, models have begun to incorporate the new pieces of evidence and started to describe a more complex historical ecology, in line with the view of a resilient society that suffered genocide after the contact with Europeans. Uncertainties affecting the archaeological evidence contribute to the formulation of contradictory narratives. Surprisingly, no agent-based models have been applied to Easter Island. I argue that these tools offer appealing possibilities for overcoming the limits of dynamic systems models and the uncertainties in the available archaeological data.