With recent developments in higher-order calculations, the theoretical uncertainty of several key Standard Model observables are now dominated by the uncertainties in fundamental parameters, such as the strong coupling and quark masses. I will describe a new strategy for the precise extraction of the strong coupling, alpha_s, from ratios of moments of the charm- and bottom-quark vector correlators. These correlators can be reliably calculated in QCD and their perturbative expansion is known up to four loops, or next-to-next-to-next-to-leading order (N3LO).
Experimentally, these moments can be extracted from measurements of e^+e^- to hadrons cross sections. I will discuss the perturbative behaviour of these recently introduced moments in the light of a calculation performed in the large-beta_0 limit of QCD. Analogous extractions of the strong coupling from the pseudo-scalar charm correlator with lattice QCD data will also be discussed.