The cosmic large-scale structure (LSS) provides a rich trove of information to probe the origin of the universe, its evolution and its constituents. The forthcoming stage-IV galaxy surveys are poised to deliver an unprecedented volume of high-precision data, holding the promise of constraining deviations from the LCDM model at the percent level and providing exciting opportunities to search for imprints of new physics. Exploiting these rich datasets to their full potential, however, is contingent upon developing new analysis technique, beyond the current state-of-the-art, to optimally extract the non-Gaussian information of the LSS. In this talk, I will discuss some of the recent works aiming at determining the information content of several summary statistics beyond the galaxy power spectrum when applied to the existing datasets. Additionally, I will describe the potential of simulation-based inference in extracting cosmological information on scales beyond the reach of the standard analyses.
