|“||Rossi, I appreciate the offer. I do. But I can't sit around brainstorming about these guys. I need the chase.||”|
— Alvez in "The Crimson King"
Alvez was born in the Bronx borough of New York City, New York. He described his mother as having a very intimidating stare. Inspired by his father's military service, he joined the U.S. Army and served as a part of the 75th Rangers Regiment in Iraq. He had a number of specialties, including animal training. After he was discharged, Alvez joined the FBI and worked in several different divisions before being assigned to its Fugitive Task Force, where he became responsible for capturing fugitives on the run. While training with the Task Force, he studied Calvin Shaw, a disgraced former FBI agent convicted of murdering his confidential informant. Later, one of Alvez's targets was a man named Daniel Cullen, a.k.a. "The Crimson King". During the manhunt, the team could never get a positive identification on Cullen during his crimes, so Alvez's partner Phil Brooks went undercover to lure him out. The operation was a success, and Cullen was recaptured, but not before he had managed to severely torture Phil. The incident traumatized Alvez ever since.
Between the events of "The Storm" and "The Crimson King," Alvez helped the BAU apprehend eight of thirteen serial killers who escaped from prisons during an attempted terrorist attack. In The Crimson King, Alvez helped catch a ninth serial killer, who turned out to be Cullen, along with a man named Brian Phillips, who was forced to become Cullen's copycat by escaped serial killer by proxy Peter Lewis. After Peter escaped, Hotch hired him into the BAU to assist in the manhunt for Peter.
- His sidearm is a SIG Sauer P226R.
- He owns a Belgium Tervuren named Roxy ("Taboo"). He mentions adopting her to help him adapt to civilian life after he was discharged. ("Dust and Bones")
- He understands some Latin ("Alpha Male").
- Like David Rossi, he likes to play video games. He mentions an interest in flight simulator and virtual reality games ("Killer App").
- According to his old partner Phil, Alvez is a terrible cook. ("Dust and Bones")
- He is the first member of the BAU to have been demoted within the team. ("Luke")