W. Benz (University of Bern, Center for Space and Habitability, Bern, Switzerland),
S. Ida (Tokyo University of Technology, Earth and Planetary Science, Japan),
Y. Alibert (University of Bern, Physikalisches Institut, Center for Space and Habitability, Switzerland),
D. Lin (University of Santa Cruz, Astronomy, United States),
C. Mordasini (MPIA, Germany)

The common existence of exoplanets and their rich structural and dynamical diversity indicates that their formation is a robust process, their evolution is driven by many competing physical processes and their destiny is determined by a wide range of boundary conditions. Population synthesis models provide a useful tool for the interpretation of exoplanets' present-day properties and the understanding of the dominant effects at each stages of their evolutionary paths. They also generate testable predictions which can be used to guide future observational strategy and model upgrades. The construction of comprehensive models and the exploration of the vast parameter space is still in a developmental stage. We review here the present status of this approach including 1) an exhaustive account of potentially relevant physical processes, 2) a summary of the quantitative prescriptions which are introduced to approximate the consequence of each effect, 3) a report on various computational methods to simulate statistical distributions, and 4) a compilation of the assumed boundary and initial conditions. We outline some outstanding theoretical uncertainties and accentuate the need of some critical observational calibrations. We confront the results of some simulated planetary census with existing data and present both the successful reproduction and disagreements between current versions of population synthesis models and observations. We identify which results can be considered reliable and which are still based on unknown processes and/or parameters. Finally, we suggest future theoretical and observational investigations that can improve the reliability of the models.

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