Galileon theories provide a useful testing ground for understanding Effective Field Theories (EFTs), both as modified-gravity models and as particle theories with nontrivial higher-derivative interactions. These higher-derivative terms are essential for ensuring local scale screening, but they also render these theories not technically well-posed. This is not an issue when treating them as valid EFTs, however, it becomes a major issue when numerically simulating their dynamics: the nonlinear evolution of Galileons excites high-frequency modes that rapidly destabilize the computation. I will present three methods we developed to regulate these high-k modes and enable stable evolution of Galileon dynamics. I will compare the performance and limitations of each approach, and show the first fully nonlinear simulations of the quartic Galileon.