  Through a large ensemble of Gaussian realisations and a suite of large-volume
N-body simulations, we show that in a standard LCDM scenario, supervoids and
superclusters in the redshift range $z\in[0.4,0.7]$ should leave a {\em small}
signature on the ISW effect of the order $\sim 2 \mu$K. We perform aperture
photometry on WMAP data, centred on such superstructures identified from SDSS
LRGs, and find amplitudes at the level of 8 -- 11$ \mu$K -- thus confirming the
earlier work of Granett et al 2008. If we focus on apertures of the size
$\sim3.6\degr$, then our realisations indicate that LCDM is discrepant at the
level of $\sim4 \sigma$. If we combine all aperture scales considered, ranging
from 1\degr--20\degr, then the discrepancy becomes $\sim2\sigma$, and it
further lowers to $\sim 0.6 \sigma$ if only 30 superstructures are considered
in the analysis (being compatible with no ISW signatures at $1.3\sigma$ in this
case). Full-sky ISW maps generated from our N-body simulations show that this
discrepancy cannot be alleviated by appealing to Rees-Sciama mechanisms, since
their impact on the scales probed by our filters is negligible. We perform a
series of tests on the WMAP data for systematics. We check for foreground
contaminants and show that the signal does not display the correct dependence
on the aperture size expected for a residual foreground tracing the density
field. The signal also proves robust against rotation tests of the CMB maps,
and seems to be spatially associated to the angular positions of the supervoids
and superclusters. We explore whether the signal can be explained by the
presence of primordial non-Gaussianities of the local type. We show that for
models with $\FNL=\pm100$, whilst there is a change in the pattern of
temperature anisotropies, all amplitude shifts are well below $<1\mu$K.
