  We overview a series of recent works addressing numerical simulations of
partial differential equations in the presence of some elements of randomness.
The specific equations manipulated are linear elliptic, and arise in the
context of multiscale problems, but the purpose is more general. On a set of
prototypical situations, we investigate two critical issues present in many
settings: variance reduction techniques to obtain sufficiently accurate results
at a limited computational cost when solving PDEs with random coefficients, and
finite element techniques that are sufficiently flexible to carry over to
geometries with random fluctuations. Some elements of theoretical analysis and
numerical analysis are briefly mentioned. Numerical experiments, although
simple, provide convincing evidence of the efficiency of the approaches.
