Subsalt imaging has been a long-term challenge for the oil and gas industry. The substantial progress made in data acquisition and imaging since the late 1990s has made some subsalt imaging problems tractable, but building earth models that enable imaging under complex salt remains a challenge. Labor-intensive workflows remain industry standard practice. Not only are these costly and time consuming, they have also performed poorly in many areas of economic interest. Various automatic model-building tools have been proposed to overcome these disadvantages. One such tool, full-waveform inversion (FWI), has already revolutionized velocity-model building in areas with shallow gas. Prior to 2006, imaging in these areas had been considered challenging and labor intensive, just as imaging under complex salt remains today. Modeling indicates that low frequencies and wide offsets may be the key to success when building velocity models using FWI. Just how low and how wide that may be required for FWI success depends on the particular problem. At the Atlantis Field in the deepwater Gulf of Mexico we recently acquired wide-offset ocean-bottom-node data with conventional airguns. By taking care during the acquisition, we recorded usable signal down to a lower frequency than previously achieved. We then applied FWI to the resulting data set and used the resulting velocity model, unmodified, to reverse time migrate the seismic data. It produced some of the best subsalt images of the Atlantis reservoir structure ever seen. Furthermore, the FWI velocity model revealed several major interpretation errors in the legacy salt model; thus the FWI result also offered an excellent basis for updating the salt model with the conventional workflow. These results demonstrate that with appropriate seismic data to support it, and with due care taken during processing and inversion, FWI truly offers a paradigm shift in model building and imaging in areas of complex salt.