  We review the development of update schemes for quantum lattice models
simulated using world line quantum Monte Carlo algorithms. Starting from the
Suzuki-Trotter mapping we discuss limitations of local update algorithms and
highlight the main developments beyond Metropolis-style local updates: the
development of cluster algorithms, their generalization to continuous time, the
worm and directed-loop algorithms and finally a generalization of the flat
histogram method of Wang and Landau to quantum systems.
