Large galaxy surveys probe the cosmic large-scale structure via the clustering of galaxies and the weak gravitational lensing effect, which are the most promising cosmological probes to reveal the nature of dark matter and dark energy, and to discover new physics beyond the concordance model of the Universe. This has prompted huge investment into new projects, which will culminate in the 2020s with surveys conducted by the ESA Euclid satellite and the Large Synoptic Survey Telescope that will cover large parts of the sky. However, the invaluable cosmological signals cause only subtle changes to a very large, noisy dataset. Already in current precursor surveys, it is, therefore, proving challenging to distinguish them from spurious measurements, astrophysical processes of galaxies, or inaccuracies in the data analysis. In my talk, I will highlight current key challenges of large-scale structure cosmology and show that a joint analysis of galaxy clustering and weak lensing is vital to obtain robust constraints on fundamental physics.