The effect of Reynolds number (Reτ) on drag reduction using spanwise wall oscillation is studied through direct numerical simulation of incompressible turbulent channel flows with Reτ ranging from 200 to 2000. For the nondimensional oscillation period T+ = 100 with maximum velocity amplitude A+ = 12, the drag reduction (DR) decreases from 35.3% ± 0.5% at Reτ = 200 to 22.3% ± 0.7% at Reτ = 2000. The oscillation frequency ω+ for maximum DR slightly increases with Reτ, i.e., from ω+ ≈ 0.06 at Reτ = 200 to 0.08 at Reτ = 2000, with DRmax=23.2%±0.6%. These results show that DR progressively decreases with increasing Reτ. Turbulent statistics and coherent structures are examined to explain the degradation of drag control effectiveness at high Reτ. Fukagata, Iwamoto, and Kasagi analysis in combination with the spanwise wavenumber spectrum of Reynolds stresses reveals that the decreased drag reduction at higher Reτ is due to the weakened effectiveness in suppressing the near-wall large-scale turbulence, whose contribution continuously increases due to the enhanced modulation and penetration effect of the large-scale and very large-scale motions in the log and outer regions. Both the power-law model (DRâ Reτ-γ) and the log-law model [DR = f(Reτ, ΔB), where ΔB is the vertical shift of the log-law intercept under control] are examined here by comparing them with our simulation data, from these two models we predict more than 10% drag reduction at very high Reynolds numbers, say, Reτ = 105.