How to prepare quantum Gibbs states or ground states on a quantum computer? A natural candidate is quantum Gibbs sampling, a quantum analog of classical Monte Carlo algorithms or, put differently, an algorithmic implementation of physical thermalization in open systems. Unfortunately, satisfactory construction for quantum Gibbs samplers has been missing for the past decade due to technical obstacles associated with energy uncertainty. Today, I will first present an efficient construction of quantum Gibbs samplers with provable guarantees depending on the mixing time. Second, we show fast mixing, assuming the Eigenstate Thermalization Hypothesis (ETH). The talk is based on joint works with Fernando Brandao, Andras Gilyen, and Michael Kastoryano.