When driving in the Northern parts of Mexico, you see many cars with license plates from the United States. Some are people who cross the border into the United States frequently and some are permanent residents of Mexico and have brought their vehicle down from the U.S. While many people don’t do this, Mexico actually has a process to legally bring a foreign plated vehicle into the country. (NOTE: If you do bring your car into Mexico, you must purchase a Mexican auto insurance policy: federal law requires third-party liability insurance on federal roads (Ley de Caminos, Puentes y Autotransporte Federal, art. 63 Bis), and Baja Bound's FAQ says your US or Canadian policy is not considered proof of financial responsibility under Mexican law.)
As a foreigner, you can bring one U.S. or Canadian car into Mexico on a temporary import permit (TIP) issued by Banjercito. A foreign vehicle driven beyond the border strip needs the permit, applied for online at Banjercito's site 60 to 7 days ahead or at the border. The requirements are a passport, a foreign driver's licence, a migration document, the title or registration in your name, lease or credit papers if applicable, a signed return declaration, a fee, and a deposit by model year (Consulate General of Mexico in Montreal). The permit carries a maximum return date, and Banjercito refunds your deposit only once the vehicle's definitive return is registered before that date (gob.mx/banjercito). An expired permit while the car is still in Mexico can mean impound and a fine, and the permit can't be returned through consulates (Consulate General of Mexico in Montreal). Don't leave the car in Mexico past that date.
If you hold or are applying for Mexican residency, ask INM and a Mexican customs broker what the rules are for your vehicle before you rely on a tourist permit; the Banjercito page says the service is exclusively for Mexicans resident abroad and tourists (foreigners).
There are parts of Mexico where these rules vary. The border strip extends 21 km into Mexico and includes all of Baja California state and Quintana Roo; entering beyond it means screening by Customs and INM (Consulate General of Mexico in Montreal). You do need to keep your registration stickers current on the vehicle, and keep in mind that if you decide to drive beyond the strip into mainland Mexico, you will now be subject to the rules discussed above. In Sonora, a free-circulation zone running from the border to km 98 of Highway 15 at Empalme needs no permit; the rest of the state takes the Only Sonora permit, which lists a current vehicle insurance policy among its requirements and is valid for up to 180 days (Sonora state government).
Ready to sort the insurance? Price a Mexican policy.