We study the large-scale structure of the Universe using the analytical technique of the consistency relations which enable to compute the squeezed bispectrum of correlation functions using symmetries of the system at hand. We study their consequences for bias models, non-perturbative models of structure formation and modified gravity. We compute the squeezed limit of the bispectrum of galaxy number counts, the quantity that galaxy surveys measure. We also compute the contamination to the non-Gaussian parameter fNL that relativistic effects produce. These are crucial if the goal of reaching a constraint on fNLloc of order unity is to be attained. Finally, we compute the squeezed bispectrum of the cross-correlation between cosmic microwave background temperature and two po- larization modes. The measurement of such correlation might be useful for distinguishing between a primordial gravitational waves background and polarization from galactic dust.