Developing non-perturbative methods might be crucial for understanding inflation and its predictions. In this talk, I will present a nonlinear study of the inflationary epoch of the Universe based on numerical lattice simulations. I will first focus on a model known as axion inflation, where the inflaton is coupled to a gauge field via Chern-Simons interaction. As a second example, I will consider a single-field model with a resonant feature in the potential. I will show that, in both cases, nonlinear effects have important consequences for the inflationary dynamics. This makes the lattice simulation crucial to understand the predictions of these models, both for large-scale observables (such as large-scale structure and CMB) and small-scale observables (primordial black holes and gravitational wave backgrounds).