This talk addresses the paleotectonic and paleogeographic evolution of the Greater Gulf of Mexico, covering the Gulf itself along with the Jurassic and Laramide events in Mexico and the progressive collision of the Antilles Arc with southern and eastern Yucatan and then the Bahamas Platform. An integrated evolutionary model for Gulf opening, supported by aeromagnetic and regional seismic reflection data sets, is set within the framework provided by Atlantic opening kinematics and the history of Caribbean-North American relative plate motion. For the Gulf of Mexico, we will review the extent of oceanic crust, image the sub-salt section, discuss pros and cons of various rift models, assess early subsidence history and some aspects of ongoing debate, timing of salt deposition in relation to basement tectonics, and some pertinent aspects of Cretaceous and Tertiary depositional history. For the Caribbean story along the southern and southeastern Gulf of Mexico, we document first arrival of flysch deposition into the Gulf margins, the timing of arc-continent collisions, and the opening of the Yucatan Basin which played an important role in the collision of the Cuban Arc with the Bahamas. We summarise what we can be confident about, what we shouldn't be confident about (but sometimes are), what is widely believed but is demonstrably wrong, and what remains unexplained. This talk is an appraisal of where we stand today and where we could continue to investigate.