Cosmological structure formation is the process, driven by gravity, that evolves the density perturbations in the early Universe into the field of galaxies and matter that we observe today. Understanding this process in detail can help answer questions relevant for fundamental physics – such as constraining the nature of Dark Energy and Dark Matter, and measuring the total mass of the Standard Model neutrinos. In this talk, I will first introduce the “Standard Model” of cosmological structure formation, and the tools that we employ to study this process, particularly in the nonlinear regime. I will then focus on two specific examples of how cosmological measurements can help pin down questions in particle physics. First, I will describe how the mass of the SM neutrinos affects structure formation, the effort over the last decade to incorporate these effects into nonlinear simulations, and how cosmological measurements in the next decade are poised to measure the absolute mass scale, and pin down the neutrino mass hierarchy. Second, I will explore some of the cosmological signatures of strong (non-gravitational) interactions of Dark Matter. I will discuss how these effects can be studied through simulations, as well as how observations from current and planned cosmological surveys can be used to very strongly constrain such models.