This document provides a comprehensive summary of the state-of-the-art, challenges, and prospects in the experimental and theoretical study of the strong coupling αs. The current status of the seven methods presently used to determine αs based on: (i) lattice QCD, (ii) hadronic τ decays, (iii) deep-inelastic scattering and parton distribution functions fits, (iv) electroweak boson decays, hadronic final-states in (v) e+e-, (vi) e-p, and (vii) p-p collisions, and (viii) quarkonia decays and masses, are reviewed. Novel αs determinations are discussed, as well as the averaging method used to obtain the PDG world-average value at the reference Z boson mass scale, αs(mZ2). Each of the extraction methods proposed provides a "wish list" of experimental and theoretical developments required in order to achieve an ideal permille precision on αs(mZ2) within the next 10 years