Highly accurate equilibrium molecular structures have been determined for the molecules cyclobutene, 1,2-difluorocyclobutene, 1,2-dicyanocyclobutene, trans-3,4-difluorocyclobutene, 1,4,4-trifluorocyclobutene, 3,3,4,4-tetrafluorocyclobutene, 1,2-dichloro-3,3,4,4-tetrafluorocyclobutene, hexafluorocyclobutene, bicyclo[2.2.0]hex-1(4)-ene, and octafluorobicyclo[2.2.0]hex-1(4)-ene at the CCSD(T) level employing basis sets up to cc-pCVQZ. The resulting definitive structural parameters, those obtained with basis sets of at least cc-pVTZ quality, support several investigations of these species employing microwave (MW) spectroscopy, at the best levels with an average error of only about 3 MHz for the rotational constants. Nevertheless, the computations also point out inadequacies of some of the experimental structural parameters. Vibrationally averaged distances and rotational constants have been obtained at the 6-31G*RHF level. Careful interpretation of the equilibrium and vibrationally averaged theoretical results point out problems with gas electron diffraction (GED) investigations of the molecular structure of hexafluorocyclobutene and 1,2-dichloro-3,3,4,4-tetrafluorocyclobutene. Most importantly, the computations prove that the length of the C-C bond opposite to the double bond becomes shorter upon fluorination and not longer, as the GED investigations have indicated.