Computationally intensive methods are becoming increasing popular within statistical ecology for analysing complex stochastic systems. Particular attention will focus on capture-recapture (and/or tag-recovery) data. We will concentrate on the use of Bayesian methods within this area and the (reversible jump) Markov chain Monte Carlo algorithm, for exploring the posterior distribution of interest. A number of issues will be discussed, including model discrimination and model-averaging, incorporating individual heterogeneity and dealing with missing data. Real data sets will be considered, illustrating the application and implementation of these methods and demonstrating the increased understanding of the systems obtained through the analysis. Areas of continuing and future research will also be discussed.