This paper takes the reader on a journey through the history of Bayesian computation, from the 18th century to the present day. Beginning with the one-dimensional integral first confronted by Bayes in 1763, we highlight the key contributions of: Laplace, Metropolis (and, importantly, his coauthors!), Hammersley and Handscomb, and Hastings, all of which set the foundations for the computational revolution in the late 20th century-led, primarily, by Markov chain Monte Carlo (MCMC) algorithms. A very short outline of 21st century computational methods-including pseudo-marginal MCMC, Hamiltonian Monte Carlo, sequential Monte Carlo, and the various 'approximate' methods-completes the paper.