During my thesis, I have worked on theoretical aspects of the large scale structure of the Universe. Clustering statistics of galaxies provide a wealth of information both on the initial conditions of cosmic structure formation and on its subsequent gravitational evolution. Extracting robust information from galaxy correlations presents several challenges, of which "galaxy bias" is one of the most significant: the relation between the observed galaxies and the underlying mass distribution generally is non-linear and scale-dependent. In this thesis, I have investigated this relation at the level of dark matter halos, which are the environments that harbor galaxies and clusters, using analytic and numerical approaches. Understanding the clustering properties of the late Universe allows also to glimpse the physics of the very early moments of history of the Universe. I have studied how to constrain signatures of primordial non-Gaussianity, namely if the random seeds of the initial perturbations are to be described with higher than 2-point statistics, from observations of the late Universe.