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Individual-based models (IBMs) of complex systems emerged in the 1960s and early 1970s, across diverse disciplines from astronomy to zoology. Ecological IBMs arose with seemingly independent origins out of the tradition of understanding the ecosystems dynamics of ecosystems from a 'bottom-up' accounting of the interactions of the parts. Individual trees are principal among the parts of forests. Because these models are computationally demanding, they have prospered as the power of digital computers has increased exponentially over the decades following the 1970s.This review will focus on a class of forest IBMs called gap models. Gap models simulate the changes in forests by simulating the birth, growth and death of each individual tree on a small plot of land. The summation of these plots comprise a forest (or set of sample plots on a forested landscape or region). Other, more aggregated forest IBMs have been used in global applications including cohort-based models, ecosystem demography models, etc. Gap models have been used to provide the parameters for these bulk models. Currently, gap models have grown from local-scale to continental-scale and even global-scale applications to assess the potential consequences of climate change on natural forests. Modifications to the models have enabled simulation of disturbances including fire, insect outbreak and harvest.Our objective in this review is to provide the reader with an overview of the history, motivation and applications, including theoretical applications, of these models. In a time of concern over global changes, gap models are essential tools to understand forest responses to climate change, modified disturbance regimes and other change agents. Development of forest surveys to provide the starting points for simulations and better estimates of the behavior of the diversity of tree species in response to the environment are continuing needs for improvement for these and other IBMs.