In statistical physics, many particle models are described by an interaction energy determined by the Coulomb potential, or more generally an inverse power law called a Riesz potential. I will discuss the interplay of entropy, energy, and functional inequalities in establishing the mean-field convergence/propagation of chaos for the dynamics of such interacting particle systems. I will also discuss the role of the trend to equilibrium for the mean-field equation and how it allows to deduce uniform-in-time convergence results or even establish the generation of chaos.