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Theoretical predictions for particle production cross sections and decays at colliders rely heavily on perturbative Quantum Chromodynamics (QCD) calculations, expressed as an expansion in powers of the strong coupling constant $α_s$. The current $\mathcal{O}(1\%)$ uncertainty of the QCD coupling evaluated at the reference Z boson mass, $α_s(m_Z) = 0.1179 \pm 0.0009$, is one of the limiting factors to more precisely describe multiple processes at current and future colliders. A reduction of this uncertainty is thus a prerequisite to perform precision tests of the Standard Model as well as searches for new physics. This report provides a comprehensive summary of the state-of-the-art, challenges, and prospects in the experimental and theoretical study of the strong coupling. The current $α_s(m_Z)$ world average is derived from a combination of seven categories of observables: (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. We review the current status of each of these seven $α_s(m_Z)$ extraction methods, discuss novel $α_s$ determinations, and examine the averaging method used to obtain the world-average value. Each of the methods discussed provides a ``wish list'' of experimental and theoretical developments required in order to achieve the goal of a per-mille precision on $α_s(m_Z)$ within the next decade.