In this chapter we present computational Monte Carlo methods to sample from probability distributions, including Bayesian posteriors, that do not permit direct sampling. In doing so, we introduce the basis for Monte Carlo and Markov chain Monte Carlo sampling schemes and delve into specific methods. These include, at first, samplers such as the Metropolis–Hastings algorithms and Gibbs samplers and discuss the interpretation of the output of these samplers including the concept of burn-in and sample correlation. We also discuss more advanced sampling schemes including auxiliary variable samplers, multiplicative random walk samplers, and Hamiltonian Monte Carlo.