In Sicario, the word "Medellin" really confused me. I believe it's Alejandro's (Del Torro) last name, and Matt Graver (Brolin) says that it refers to a particular era in Mexico (I forgot the exact words) when Kate Macer (Blunt) asks what it means. Then in the end when Alejandro is pointing his gun at the cop after he exits the tunnel being raided, the cop quietly says "Medellin...". Is he saying Alejandro's name? If so how did he know who it was? If that's his last name why does IMDB only refer to him as Alejandro? If the word refers to an era, why would the cop just muter that to himself?
Medellín refers to the Medellín Cartel, which was a Colombian drug cartel that operated from 1972-1993 and was probably the largest ever to have existed.
I don't have all the answers, but here's the evidence from the movie:
After the meeting with the US Marshals:
Macer: "Where were you sent from?"
Alejandro: "Cartagena" (a city in Colombia)
Alejandro also says he was a prosecutor, working for Mexico.
During the interrogation of Guillermo:
Graver: "Ah Alejandro, I think he remembers you"
Alejandro: "Now you'll learn what's hell in Yankee land"
Guillermo: "No Medellín"
After the tunnel firefight:
Silvio to Alejandro: "Medellín?"
Graver and Macer after the firefight:
Macer: "What is Medellín?"
Graver: "Medellín refers to a time. When one group controlled every aspect of the drug trade. Providing a measure of order that we could control. What you saw there was Alejandro working toward returning that order"
Macer: "Alejandro works for the fucking Colombian cartel"
Graver: "Alejandro works for anyone who will point him toward the people who made him"
So, Graver here is saying that Alejandro does not work for the Colombian cartel (though may have earlier in order to get closer to the Alarcon cartel).
According to Wikipedia, Alejandro's surname is Gillick.