This paper deals with anisotropic mesh adaptation applied to unsteady inviscid CFD simulations. Anisotropic metric-based mesh adaptation is an efficient strategy to reduce the extensive CPU time currently required by time-dependent simulations in an industrial context. In this work, we detail the time-accurate extension of multi-scale anisotropic mesh adaptation for steady flows [35] (a control of the interpolation error in norm to capture all the scales of the solution contrary to the norm that only focuses on the larger scales) to unsteady flows when time advancing discretizations are considered. This is based on a space–time error analysis and an enhanced version of the fixed-point algorithm [3]. We also show that each stage – remeshing, metric field computation, solution transfer, and flow solution – is important to design an efficient time-accurate anisotropic mesh adaptation process. The parallelization of the whole mesh adaptation platform is also discussed. The efficiency of the approach is emphasized on three-dimensional problems with convergence rate and CPU time analysis.