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 $zin[0.4,0.7]$ 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 $sim3.6degr$, then our realisations indicate that LCDM is discrepant at the level of $sim4 sigma$. If we combine all aperture scales considered, ranging from 1degr--20degr, then the discrepancy becomes $sim2sigma$, 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 $1.3sigma$ 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 $<1mu$K.
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