Improving cosmological constraints from galaxy clustering presents several challenges, particularly in extracting information beyond the power spectrum because of the complexity of higher-order n-point function analyses. In this talk, I will introduce novel inference techniques that go beyond the current state of the art. Using LEFTfield, a Lagrangian forward model based on the Effective Field Theory of Large-Scale Structure (EFTofLSS) and the bias expansion, I will present both simulation-based inference (SBI), which enables cosmological inference from summary statistics in simulations without explicit analytical likelihoods or covariance matrices, and field-level inference (FLI), where a field-level likelihood is used to directly analyze the full 3D galaxy density field rather than compressed statistics. I will discuss the main advantages and challenges of these approaches, and use them to study the cosmological information content of galaxy clustering.