Born in the Bronx borough of New York City, New York, Alvez served in the U.S. Army as a part of the 75th Rangers Regiment and had a number of specialties, including animal training. After he was discharged, he joined the FBI and was 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 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.