In this survey we have provided an outline of Markov chain Monte Carlo methods. These methods provide a set of general recipes for sampling intractable multivariate distributions and have proved vital in the recent virtually revolutionary evolution and growth of Bayesian statistics. Refinements and extensions of these methods continue to occur. Two recent developments are the slice sampling method discussed by [41], [20] and [51] and the perfect sampling method proposed by [44]. The slice sampling method is based on the introduction of auxiliary uniform random variables to simplify the sampling and improve mixing while the perfect sampling method uses Markov chain coupling to generate an exact draw from the target distribution.