The Bayesian paradigm provides a coherent and unified approach to problems of statistical inference such as parameter estimation, hypothesis testing, prediction, or model discrimination within a decision-theoretic framework. Bayesian inference for complex models heavily relies on computationally intensive methods. At the IFAS we are currently working on Bayesian modelling of categorical and mixed data, Bayesian estimation of mixture and treatment effects models, Bayesian model selection and approximate Bayesian computation for models with intractable likelihoods.