Determining the strong coupling: status and challenges

The `XIIIth Quark Confinement and the Hadron Spectrum' conference (Confinement 2018) contained a `Round Table Discussion' on the status of the determinations of the strong coupling $\alpha_s(m_Z)$ as well as prospects for future improvements. In this contribution, we summarize the different aspects of the discussion. In particular, we cover $\alpha_s$ determinations from inclusive observables, such as the hadronic decays of the $Z$ boson and the $\tau$ lepton; from global fits of parton distribution functions (PDFs); from high-energy collider observables, and from event shapes; as well as from various observables computed by lattice QCD, specifically from the QCD static energy. There is overall good agreement between these various determinations, but there are also outliers, differing from the world average by up to $-5\%$. Nevertheless, the general agreement constitutes a beautiful and significant test of the detailed nature of the strong interactions, and provides a crucial input for high-precision calculations in QCD and beyond.