Finite mixture models have been used for more than 100 years, but have seen a real boost in popularity over the last decades due to the tremendous increase in available computing power. These models find widespread application in many areas of applied statistics. Three different areas of application can be distinguished: one major reason is to deal with unobserved heterogeneity, likely to be present in most data sets arising in marketing, economics, medicine or in the social sciences. A second application of mixture models is model-based clustering, classification and discrimination of socio-economic and related data. The third application has the purpose to estimate and approximate an unknown density function in a semi-parametric way. The mixture modeling group at the IFAS is currently working on Bayesian and frequentist estimation of finite mixture models, model identification and inference as well as on different applications of mixture models.