This paper investigates the use of computational Bayesian methods for multiuser detection (MUD) of synchronous direct-sequence code-division multiple access (DS-CDMA) systems. The Markov chain Monte Carlo (MCMC) multiuser detection methods proposed in this paper are iterative, and offer near-optimal performance with manageable complexity even at high system loads. Moreover, posterior symbol probabilities produced by the detector are suitable for use as prior probabilities for soft-input channel decoders.