We study the properties of mean-field Gibbs measures with possibly singular interactions. We prove a law of large numbers and a quantitative central limit theorem with optimal rates in the full subcritical regime of temperatures T > Tc. Our treatment of the singular interaction borrows ideas from Nelson?s construction of the $\phi^4_2$ Euclidean quantum field theory and our ability to capture the entire subcritical regime relies on a sharp non-asymptotic large deviations-type estimate. Finally, we derive the quantitative CLT using a variant of Stein?s method. As a by-product of our results, we show that the free energy of the mean-field Coulomb gas is bounded, thus improving on the logarithmically growing bound obtained by Serfaty and Rosenzweig. This is joint work with Matías G. Delgadino (UT Austin).