Mexico was a country to the south of the United States. While it was never annexed as Canada was, the US, seeking to protect business interests and their oil supply, put a lot of pressure on Mexico in 2051 and finally invaded it, though it is unknown whether total annexation had occurred.
The country also had a major company named Petro-Chico, a petroleum corporation that was a subsidiary of Poseidon Energy, and had oil supplies all along the Rio Grande, and owned all of the oil flowing up to Las Vegas. Petro-Chico had adminstrative holdings in the states of Veracruz, Puebla, and Hidalgo.
Timeline
2042 - A major earthquake takes place in Mexico City. The Mister Handy general construction robot becomes the leader in sales in Mexico. (source: Mr. Handy design document)
2051 - Seeking to protect business interests and their oil supply, the United States began to exert increasing pressure on Mexico, citing the political instability and pollution stemming from Mexico as a threat to the United States. Various economic sanctions served to destabilize Mexico, and the United States military entered Mexico to keep the oil refineries running and ensure that oil and fuel continued to make their way north across the border (at Mexico's expense). (appears in the Fallout Bible timeline)
The following is based on Van Buren design documents and is not canon.
2066 - Resource rioting occurs in Denver. Midwest USA and Mexico start having food shortages and can't supply Denver with the food it needs. Food riots occur, and the National Guard is called in. (source: Denver design document)
End of information based on Van Buren design documents