Spoilers ahead.
Emily Blunt (Kate) is a FBI agent that specializes in kidnappings. During a raid on a kidnap case they discover scores of dead bodies in the walls and spaces of the house. It turns out it is a home owned by a man called Diaz.. who is sort of the Executive Officer on the American side for a drug cartel. Diaz’s brother Guillermo is kind of the strong arm man in Juarez in Mexico and the whole carted is run by their cousin Silvio, who they call “a ghost” meaning they do not know much about him not even where he lives.
Kate is asked to volunteer for a special task force run by an “operative from the DoD” named Matt (Josh Brolin). She does and he tells her they are going into Juarez to extract Guillermo. On the ride over she meets who is introduced as “a watchdog” (Alejandro played by Benicio Del Toro). They extract Guillermo, get in a firefight on the bridge from el Paso then Alejandro water boards him for information. They discover there is a “tunnel” that leads from Arizona to Mexico that Diaz uses to run drugs. They do not know the exact location. Supposedly Guillermo does not know that either or at least he did not tell.
Matt has immigration agents hold a group of illegal immigrant migrant workers in another part of Arizona for questioning and he, Alejandro, Kate and her FBI partner Reggie go to question them. They are able to “recruit” a handful of them that are able to help them pinpoint the location of the tunnel (because they know the area having crossed the border illegally many times) presumably in exchange for green cards. They also find out that a certain bank is where Diaz makes all the drug money deposits. They then decide to “disrupt” Silva’s operation to the point where Diaz will be “called to Silva” presumably to explain why everything is so disrupted or perhaps to plan a counter attack and then they can find him. So they arrest the mules making the cash deposits. Kate thinks this is enough to arrest Diaz but Matt warns her not to try. She tries anyway and nearly gets killed by a dirty cop on Diaz’ payroll before Alexandro saves her.
Because of the arrest at the bank they are able to freeze all of Silva's accounts, at least with that bank totalling over 17 million (we get the impression Silva is not a major cartel but a mildly successful of one-- this adds to the confusion as to why they are so ardently seeking him) So now they get intel that Diaz is crossing the tunnel to return to Silva. They form a task force and infiltrate the tunnel to follow him. Alejandro kidnaps a drug mule on the Mexican side and using drone technology he follows Diaz. He then kills the mule and wounds Diaz, kidnapping him. He makes Diaz at gunpoint take him to Silva, kills Diaz, all of Silva’s guards then invades Silva’s mansion. He then murders Silva’s family and then finally kills Silva It is revealed that this is all in revenge because Silva killed Alejandro’s child and wife (putting her in a vat of acid when Alejandro was a prosecutor in Juarez years before).
Back on the American side Kate has had enough calling into question the legality of it all. Matt reveals that he is not DoD but CIA and their ultimate goal besides letting Alejandro get revenge is to kill off all the smaller cartels and put the Medellin Cartel back as the main one.. at least that way they “know their enemy”. He recruited Kate due to laws that require FBI agents to be on teams where ops are run on US soil.. that is the only reason. Kate states that she will blow the whistle. A day later Alejandro shows up at Kate’s home and with gun to head makes her sign a “nondisclosure agreement” and that says that everything they did was “above board and legal”. She hesitates at first then signs knowing Alexandro will kill her. He leaves her humiliated and defeated telling her that she needs to move to a small town because she is not cut out to fight the war under the “new rules”.