Many aspects of the evolution of stars, and in particular the evolution of binary stars, are beyond our ability to model them in detail. Instead, we rely on observations to guide our often phenomenological models and pin down uncertain model parameters. To do this statistically requires population synthesis. Populations of stars modelled on computers are compared to populations of stars observed with our best telescopes. The closest match between observations and models provides insight into unknown model parameters and hence the underlying astrophysics. This chapter reviews the impact that modern big-data surveys will have on population synthesis, the large parameter space problem that is rife for the application of modern data science algorithms and some examples of how population synthesis is relevant to modern astrophysics.