  In 1986, Swendsen and Wang proposed a replica Monte Carlo algorithm for spin
glasses [Phys. Rev. Lett. 57 (1986) 2607]. Two important ingredients are
present, (1) the use of a collection of systems (replicas) at different of
temperatures, but with the same random couplings, (2) defining and flipping
clusters. Exchange of information between the systems is facilitated by fixing
the tau spin (tau=sigma^1\sigma^2) and flipping the two neighboring systems
simultaneously. In this talk, we discuss this algorithm and its relationship to
replica exchange (also known as parallel tempering) and Houdayer's cluster
algorithm for spin glasses. We review some of the early results obtained using
this algorithm. We also present new results for the correlation times of
replica Monte Carlo dynamics in two and three dimensions and compare them with
replica exchange.
