The Mexican Empire was founded in time immemorial by somebody, mexicans probably. The First Doctor and his kidnapping victims traveled to Mexico and got trapped in a novelty chain restaurant called the Azteca. Through the machinations of Charlie Sheen, they were nearly sacrificed to the almighty chef in order to ensure a bountiful harvest of fresh hot tortilla chips. During this time, the Doctor got engaged to a smoking hot mexican GMILF, but his useless granddaughter and unwilling companions cockblocked him before he could get a taste of her hot chocolate, if you know what I mean.
Some time later, the Mexicans waged a bloody war populated entirely by bandito stereotypes. Arturo Villar, a totally accurate depiction of a mexican person, was one of the many soldiers kidnapped by the War Lords to take part in Malcolm Hulke's and Terrance Dicks's® The War Games©: Part One: An Unexpected Journey® In I-MAX™ 3D©. He tried desperately to get in Zoe's tight glittery panties but eventually chose to pursue an intense and passionate affair with Jamie.
In 2030, Mexico was again king of fuck mountain. A brilliant scientist and philanthropist by the name of Salamander (because, really, what would a mexican call himself?) was putting his considerable resources towards the goal of totally control of the human race. Sadly, Salamander was cursed with the shocking fate of looking like the Second Doctor. Rather than live looking like the Trout, he flung himself into the time vortex, there to be ground up into subatomic particles by the engines of eternity.
20 years later, Mexicans traveled to the moon, looking for any scrap they could sell to make the rent check this month. Instead, they found spiders that aren't spiders and a moon that isn't a moon, and they were all eaten and eviscerated. It was VNA-level dark, there were spider like creatures, and the Doctor gave Clara the shock of her life. Reminder to stay hype.