State space models provide a flexible tool for time series analysis, that are able to deal with many irregularities in time series which are difficult to cope with in classical time series analysis. Examples are missing values, structural breaks, outliers, or slowly moving changes. State space models are also easily extended to non-normal data, in particular to discrete-valued time series like time series of counts and binary time series. Whereas estimation is rather straightforward for normally distributed time series observations, state space models for discrete-valued time series are far more challenging when it comes to estimation. The MCMC group at the IFAS developed new Gibbs sampling schemes for the Bayesian estimation of state space models for discrete-valued time series. Recently, focus has shifted toward model and variable selection problems.