  We overview a series of recent works devoted to variance reduction techniques
for numerical stochastic homogenization. Numerical homogenization requires
solving a set of problems at the micro scale, the so-called corrector problems.
In a random environment, these problems are stochastic and therefore need to be
repeatedly solved, for several configurations of the medium considered. An
empirical average over all configurations is then performed using the
Monte-Carlo approach, so as to approximate the effective coefficients necessary
to determine the macroscopic behavior. Variance severely affects the accuracy
and the cost of such computations. Variance reduction approaches, borrowed from
other contexts of the engineering sciences, can be useful. Some of these
variance reduction techniques are presented, studied and tested here.
