  This review treats the mathematical and algorithmic foundations of
non-reversible Markov chains in the context of event-chain Monte Carlo (ECMC),
a continuous-time lifted Markov chain that employs the factorized Metropolis
algorithm. It analyzes a number of model applications, and then reviews the
formulation as well as the performance of ECMC in key models in statistical
physics. Finally, the review reports on an ongoing initiative to apply the
method to the sampling problem in molecular simulation, that is, to real-world
models of peptides, proteins, and polymers in aqueous solution.
