Late Pleistocene extinctions occurred globally over a period of about 50,000 years, primarily affecting mammals of > or = 44 kg body mass (i.e., megafauna) first in Australia, continuing in Eurasia and, finally, in the Americas. Polarized debate about the cause(s) of the extinctions centers on the role of climate change and anthropogenic factors (especially hunting). Since the late 1960s, investigators have developed mathematical models to simulate the ecological interactions that might have contributed to the extinctions. Here, we provide an overview of the various methodologies used and conclusions reached in the modeling literature, addressing both the strengths and weaknesses of modeling as an explanatory tool. Although late Pleistocene extinction models now provide a solid foundation for viable future work, we conclude, first, that single models offer less compelling support for their respective explanatory hypotheses than many realize; second, that disparities in methodology (both in terms of model parameterization and design) prevent meaningful comparison between models and, more generally, progress from model to model in increasing our understanding of these extinctions; and third, that recent models have been presented and possibly developed without sufficient regard for the transparency of design that facilitates scientific progress.