[4] At the 2012 Summer Olympics, competing at bantamweight, he beat American Joseph Diaz and Robenílson Vieira of Brazil but lost to Irishman John Joe Nevin 14-19 in the semifinal and won bronze.

Álvarez won the lightweight title at the 2013 AIBA World Championships, beating Joseph Cordina, Fazliddin Gaibnazarov, Saylom Ardee, Berik Abdrakhmanov and, in the final, Robson Donato Conceicao.

[4] At the 2015 Pan American Games, he won gold, beating Elvis Severino Rodriguez, Kevin Luna and Lindolfo Delgado along the way.

[4] He won the bronze medal at the men's lightweight event at the 2016 Summer Olympics, losing to Conceicao in the semifinal.

[7] At the 2019 World Championships, he fought at featherweight, beating Peter McGrail, before losing to Mirazizbek Mirzakhalilov in the final.