Excited states in the odd-odd, highly neutron-deficient nucleus 166Re have been investigated via the 92Mo(78Kr, 3p1n) 166Re reaction. Prompt γ rays were detected by the JUROGAM II γ -ray spectrometer, and the recoiling fusion-evaporation products were separated by the recoil ion transport unit (RITU) gas-filled recoil separator and implanted into the Gamma Recoil Electron Alpha Tagging spectrometer located at the RITU focal plane. The tagging and coincidence techniques were applied to identify the γ -ray transitions in 166Re, revealing two collective, strongly coupled rotational structures, for the first time. The more strongly populated band structure is assigned to the πh11/2[514]9/2− ⊗ νi13/2[660]1/2+ Nilsson configuration, while the weaker structure is assigned to be built on a two-quasiparticle state of mixed πh11/2[514]9/2− ⊗ ν[h9/2f7/2]3/2− character. The configuration assignments are based on the electromagnetic characteristics and rotational properties, in comparison with predictions from total Routhian surface and particle-rotor model calculations.