The topic of this talk lies at the intersection of (quantum) statistical physics, stochastic processes, and quantum algorithms. The algorithms that I will describe provide efficiently implementable quantum generalisations of the Metropolis algorithm for preparing quantum Gibbs (thermal) states – an essential task in quantum simulation. They could lead to one of the first useful applications of quantum computers, shed new light on how quantum systems reach equilibrium, and open new avenues for extending the rich theory of stochastic processes to the quantum domain.