This article surveys advances in the field of Bayesian computation over the past 20 years from a purely personal viewpoint, hence containing some ommissions given the spectrum of the field. Monte Carlo, MCMC, and ABC themes are covered here, whereas the rapidly expanding area of particle methods is only briefly mentioned and different approximative techniques such as variational Bayes and linear Bayes methods do not appear at all. This article also contains some novel computational entries on the doubleexponential model that may be of interest. Bayesian Computational Tools