In this talk, I will discuss the applications of the Effective Field Theory (EFT) in cosmology. In the first part, I will outline the main concepts of the non-linear cosmological perturbation theory, which provides a systematic analytic description of the clustering of matter and biased tracers on large scales. I will introduce the EFT bias expansion in the presence of line-of-sight selection effects and formulate the EFT model for the Lyman-alpha forest. Following this, I will present the one-loop EFT model for the cross-spectrum of the Lyman-alpha forest and a generic biased tracer of matter. I will demonstrate that including cross-correlations significantly improves constraints on EFT parameters compared to those obtained from individual auto-power spectra. Our EFT model fits the simulated cross-spectra with a percent level accuracy at kmax = 1 h/Mpc.

In the second part, I will introduce the EFT of dark energy approach, which provides a systematic description of linear perturbations in general scalar-tensor theories. Focusing on general Horndeski theories, I will present cosmological constraints on deviations from general relativity from the CMB, CMB lensing, CMB ISW-lensing, DESI BAO DR1, and SN Ia datasets. I will discuss the robustness of DESI's preference for evolving dark energy in light of these results.