Precision jet measurements at HERA and determination of α_s

The status is reviewed of recent high precision measurements of inclusive-jet, dijet and trijet production in deep-inelastic scattering and photoproduction by the HERA experiments H1 and ZEUS. The measurements are in good agreement with perturbative QCD calculations at next-to-leading order and are used for the extraction of the value of the strong coupling at the mass of the Z boson, \alpha_s(M_Z). The methods and results of the QCD analyses are presented and a summary of the values of \alpha_s(M_Z) from recent jet measurements at HERA is given.