Recent results on jet physics and tests of QCD from hadronic final states in $e^+e^-$ annihilation at PETRA and at LEP are reviewed, with special emphasis on hadronic event shapes, charged particle production rates, properties of quark and gluon jets and determinations of $alpha_s$. The data in the entire energy range from PETRA to LEP-2 are in broad agreement with the QCD predictions. The world summary of measurements of $alpha_s$ is updated and a detailed discussion of various methods to determine the overall error of $alpha_s (M_Z)$ is presented. The new world average is $alpha_s (M_Z) = 0.119 pm 0.004$. The size of the error depends on the treatment of correlated uncertainties.
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