The new copper(I) rhenates, CuReO4(pyz) (I) and Cu3ReO4(q6c)(2) (II) (pyz = pyrazine; q6c = quinoline-6-carboxylate), were synthesized by hydrothermal methods at 140-150 degrees C, and their structures determined via single-crystal X-ray diffraction (I, P2(1)/n, No. 14, Z = 4, a = 7.972(1) A, b = 11.928(2) A, c = 8.430(1) A, beta = 102.161(2)degrees; II, P2(1), No. 4, Z = 2, a = 8.253(2) A, b = 6.841(2) A, c = 18.256(6) A, beta = 101.37(2)degrees) and characterized by thermogravimetric analyses and UV-vis diffuse reflectance. The structure of I contains 'CuReO4' layers that are pillared through bridging pyrazine ligands via the Cu sites, while the structure of II is polar and contains chains of 'Cu2ReO4' that are condensed into layers by coordination to linear 'Cu(q6c)(2)' bridges between the chains. In contrast to air-sensitive CuReO4, both hybrid analogues are stable in air owing to a stabilization of the Cu1+ oxidation state by N-donating ligands, but decompose upon heating with the removal of the organic ligands, which for I yields crystalline CuReO4. UV-vis diffuse reflectance measurements and electronic structure calculations on all three copper perrhenates, I, II, and CuReO4, show that each exhibits an optical band gap of similar to 2.1-2.2 eV, with conduction and valence band levels that are primarily derived from the Re d(0) and Cu d(10) orbitals, respectively, and mixed with O p-orbital contributions. In contrast to the silver rhenates, which have relatively lower energy Ag d(10) orbitals, the inclusion of the organic ligands into the structures has only a very minor effect (similar to 0.1 eV) on the band gap size. The optical absorptions, in combination with the air-stable open-framework layered structures, illustrate that heterometallic Cu1+/Re7+ oxides can be promising candidates for investigating in visible-light photocatalytic reactions.