The neutron-deficient rhenium isotopes 166-17~ were investigated using reactions of 32S with monoisotopic 141pr targets. Gamma-rays following the fl-decays of 166-169Rewere measured for the first time. Four new e-rays with energies of 4.70, 4.83, 4.87, and 5.02 MeV were detected in addition to the known 5.50, 5.26, and 5.06 MeV e-rays. Alpha-decaying isomer pairs were discovered in 167Re and 169Re. The measured half-lives are 2.3(2)s for 166Re, 3.4(4)s and 6.2(5)s for 167Re, 4.4(1)s for 168Re, 8.1(5)s and 16.3(8)s for 169Re, and 9.2(2)s for iV~ The nuclear structure is discussed in terms of single-particle states.