Many of the most interesting mean-field interacting particle systems involve Riesz or inverse-power type interactions. However, it is only relatively recently that these systems have been shown to satisfy mean-field convergence in full generality. That is, as the number of particles increases, the empirical measures converge to a limiting equation. Despite this progress, proving these systems satisfy large deviation principles remains a significant open problem. Most known results, motivated by random matrix theory, focus on particles with logarithmic repulsion in 1D and are not easily adapted to more singular interactions. In this talk, I will discuss my recent work, where I combine modulated energy methods and hydrodynamic techniques to derive local large deviation estimates for repulsive, sub-Coulomb Riesz interacting systems.