Testing the initial conditions with the large-scale structure of the Universe

The possible detection of a non-Gaussian component in the Cosmic Microwave Background anisotropies by the Planck mission would constitute a major result for contemporary cosmology. Such a discovery would rule-out, per se, single- field, slow-roll, canonical model for inflation and significantly help in discriminating between high-energy models of the early Universe. On the other hand, the detection of primordial non-Gaussianity in the large-scale structure would provide a fundamental confirmation. I will review the recent but intense activity on the effects of non-Gaussian initial conditions on the galaxy and cluster distributions. I will discuss the large-scale correction to the bias of halos and the galaxy power spectrum and I will focus, in particular, on the possibilities offered by the measurement of higher-order correlation functions such as the galaxy bispectrum.