  Ab-initio studies of strongly interacting bosonic and fermionic systems is
greatly facilitated by efficient Monte Carlo algorithms. This article
emphasizes this requirement, and outlines the ideas behind the construction of
the cluster algorithms and illustrates them via specific examples. Numerical
studies of fermionic systems at finite densities and at real-times are
sometimes hindered by the infamous sign problem, which is also discussed. The
construction of meron cluster algorithms, which can solve certain sign problems
are discussed. Cluster algorithms which can simulate certain pure Abelian gauge
theories (realized as quantum link models) are also discussed.
