This paper presents the performance of the ATLAS muon reconstruction during the LHC run with [Formula: see text] collisions at [Formula: see text]-8 TeV in 2011-2012, focusing mainly on data collected in 2012. Measurements of the reconstruction efficiency and of the momentum scale and resolution, based on large reference samples of [Formula: see text], [Formula: see text] and [Formula: see text] decays, are presented and compared to Monte Carlo simulations. Corrections to the simulation, to be used in physics analysis, are provided. Over most of the covered phase space (muon [Formula: see text] and [Formula: see text] GeV) the efficiency is above [Formula: see text] and is measured with per-mille precision. The momentum resolution ranges from [Formula: see text] at central rapidity and for transverse momentum [Formula: see text] GeV, to [Formula: see text] at large rapidity and [Formula: see text] GeV. The momentum scale is known with an uncertainty of [Formula: see text] to [Formula: see text] depending on rapidity. A method for the recovery of final state radiation from the muons is also presented.