Subject to techniques of perturbative renormalization, the Standard Model makes empirical predictions that are stupendously successful. But also deeply mysterious. Not every quantum field theory (qft) is renormalizable. Indeed, most aren’t. The mystery is: why should we be so lucky, that we live in a world governed by a renormalizable qft? I explicate this Renormalizability Puzzle, and explain why Renormalization Group (RG) approaches are widely thought to resolve it. Looking under the hood of the RG resolution, I identify a load-bearing element that might not be adequate to the explanatory burden the RG resolution places upon it.