  It has been proposed that the observed dark energy can be explained away by
the effect of large-scale nonlinear inhomogeneities. In the present paper we
discuss how observations constrain cosmological models featuring large voids.
We start by considering Copernican models, in which the observer is not
occupying a special position and homogeneity is preserved on a very large
scale. We show how these models, at least in their current realizations, are
constrained to give small, but perhaps not negligible in certain contexts,
corrections to the cosmological observables. We then examine non-Copernican
models, in which the observer is close to the center of a very large void.
These models can give large corrections to the observables which mimic an
accelerated FLRW model. We carefully discuss the main observables and tests
able to exclude them.
