  The most efficient weights for Markov chain Monte Carlo calculations of
physical observables are not necessarily those of the canonical ensemble.
Generalized ensembles, which do not exist in nature but can be simulated on
computers, lead often to a much faster convergence. In particular, they have
been used for simulations of first order phase transitions and for simulations
of complex systems in which conflicting constraints lead to a rugged free
energy landscape. Starting off with the Metropolis algorithm and Hastings'
extension, I present a mini review which focuses on the explosive use of
generalized ensembles in the early 1990s. Illustrations are given, which range
from spin models to peptides.
