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Finite mixture models have been used in many fields for different purposes and under different names. Other non-exact names are model-based clustering and latent class models. This presentation gives an overview of this area. In particular, it summarizes the research that has been published both theoretical papers and in applications. A systematic literature review using the PRISMA methodology was used. The text mining analysis then identifies topics in the literature. Results show an explosion of the research in the field since 2000. Social and health sciences are the most prominent application areas, mainly focused on the detection of unobserved heterogeneity.