Model selection is the task of choosing a model from a set of candidate models. A prominent example is variable selection in regression models, where the goal is to identify the relevant regressors from a set of potential explanatory variables. Variable selection is crucial for two reasons: omission of relevant variables leads to biased estimates and inclusion of irrelevant regressors results in poor estimation precision. In a classical approach model selection is based on hypothesis testing, information criteria, like AIC and BIC or other citeria e.g. information divergence or Fisher information. In a Bayesian approach model selection can be accomplished by algorithms performing a stochastic search of the model space. Closely related is Bayesian model averaging, which allows to take into account model uncertainty. At the IFAS methods for Bayesian variable selection in generalized linear models and mixed data models as well as for model selection in random effects and state space models have been developed. Current research focuses on variable selection in treatment effects models and model selection for categorical covariates (FWF project pf.fwf.ac.at/de/wissenschaft-konkret/project-finder, opens an external URL in a new window.