Upcoming cosmological experiments aim to retrieve detailed data on the distribution of matter on the largest cosmological scales, driven by the search for physics beyond the standard models of cosmology and particle physics. To infer unknown parameters from these experiments, we need accurate predictions of the evolution of cosmic structures. For this, perturbation theory (PT) is an indispensable tool for interpreting observables across a wide range of cosmological scales. However, PT cannot accurately resolve the highly nonlinear stages of gravitational collapse of dark matter. Instead, numerical simulation techniques, typically using N-body methods, are employed. Although N-body methods are the most efficient available, they are still computationally very costly. In this talk, I will present recent avenues where insights from PT are exploited to make N-body simulations significantly more efficient.