$\alpha_s$ review (2016)

The current world-average of the strong coupling at the Z pole mass, $\alpha_s(m^2_{Z}) = 0.1181 \pm 0.0013$, is obtained from a comparison of perturbative QCD calculations computed, at least, at next-to-next-to-leading-order accuracy, to a set of 6 groups of experimental observables: (i) lattice QCD "data", (ii) $\tau$ hadronic decays, (iii) proton structure functions, (iv) event shapes and jet rates in $e^+e^-$ collisions, (v) Z boson hadronic decays, and (vi) top-quark cross sections in p-p collisions. In addition, at least 8 other $\alpha_s$ extractions, usually with a lower level of theoretical and/or experimental precision today, have been proposed: pion, $\Upsilon$, W hadronic decays; soft and hard fragmentation functions; jets cross sections in pp, e-p and $\gamma$-p collisions; and photon F$_2$ structure function in $\gamma\,\gamma$ collisions. These 14 $\alpha_s$ determinations are reviewed, and the perspectives of reduction of their present uncertainties are discussed.