Formation anisotropy should be incorporated into the analysis of controlled-source electromagnetic (CSEM) data because failure to do so can produce serious artifacts in the resulting resistivity images for certain data configurations of interest. This finding is demonstrated in model and case studies. Sensitivity to horizontal resistivity will be strongest in the broadside electric field data where detectors are offset from the tow line. Sensitivity to vertical resistivity is strongest for overflight data where the transmitting antenna passes directly over the detecting antenna. Consequently, consistent treatment of overflight and broadside electric field measurements requires an anisotropic modeling assumption. To produce a consistent resistivity model for such data, we develop and use a 3D CSEM imaging algorithm that treats transverse anisotropy. The algorithm is based on nonlinear conjugate gradients and full wave-equation modeling. It exploits parallel computing systems to effectively treat 3D imaging problems and CSEM data volumes of industrial size. We use it to demonstrate the anisotropic imaging process on model and field data sets from the North Sea and offshore Brazil. We also verify that isotropic imaging of overflight data alone produces an image generally consistent with vertical resistivity. However, superior data fits are obtained when the same overflight data are analyzed assuming an anisotropic resistivity model.