The topic of stochastic homogenization of elliptic partial differential equations in divergence form is classical. It is about the homogeneous large-scale behavior of heterogeneous media, like conductive media or elastic media, that are characterized in stochastic terms. Our interest grew out of quantifying the error scaling in the engineer's concept of a ``representative volume element'', which allows to approximately extract the homogeneous coefficients. Meanwhile, the connections with classical regularity theory (attached to the names De Giorgi, Nash, Campanato, Meyers ... ) and with concepts of concentration of measure (as for instance captured by the Logarithmic Sobolev Inequalities) have emerged in a clearer way. Not only is the regularity theory for uniformly elliptic coefficient fields a a key ingredient, but stochastic homogenization sheds a new light on a generic large-scale behavior of a-harmonic functions - which is more regular than suggested by the classical counter-examples. We also advocate to exploring more the synergies between the treatment of quenched noise (like the random coefficients in stochastic homogenization) and thermal noise (like in statistical mechanics or stochastic partial differential equations).