Performance of the muon identification and reconstruction with the ATLAS detector

We present the muon reconstruction algorithms used in ATLAS during the LHC run-1 and their performances in terms of efficiency, muon momentum scale and resolution. These performances have been measured using large calibration samples of $J/\psi$, $\Upsilon$ and $Z$ decays, which allow to control the systematic uncertainties on efficiency and on momentum scale at the per-mille level. Corrections to be applied to simulation have been derived from the performances measurements and used in physics analyses. The impact of these correction on physics measurements, and the associated uncertainties, is also presented.