Bruno Cadogan, a doctoral student in Spanish Literature at New York University, is making little progress on his dissertation, a study of Jorge Luis Borges's essays on the tango. As he wanders through the Village, a chance encounter with a specialist in Latin American culture launches him in a new direction: she suggests that he go to Buenos Aires in pursuit of the elusive tango singer Julio Martel, who voice is "like another dimension, almost supernatural," far superior to the legendary Carlos Gardel's.

Inspired by her tip, and with the help of academic grants, Bruno travels to Buenos Aires in the fall of 2001, just as the Argentine economy goes into freefall. After finding a room in a cheap boarding house, he begins to explore Buenos Aires and many of its tango salons, gathering information about Martel and hoping to meet the man who he imagines will turn his stalled dissertation around.

His search leads him into the heart of the tango world in Buenos Aires, where he makes a close study of the experts. As described in Anne McLean's splendid translation: "...the dance began with a somewhat brutal embrace. The man’s arm encircled the woman’s waist and from that moment she began to back away. She was always on the retreat. Sometimes he arched his chest forward or turned side-ways, check to cheek, while his legs sketched tangled figures that the woman would have to repeat in reverse…. It looked like athletic sex, tending towards perfection but with no interest in love."

Along the way, he finds other aficionados of Julio Martel and learns that Martel's reputation in Argentina grew during the same period that "people disappeared by the thousand," victims of the Dirty War waged by the military dictatorship from 1976-1983. Despite his growing fame, the singer suddenly stopped performing in public, and now makes only infrequent and unannounced appearances at different locations around the city. Martel seems to be tracing a secret map of the city, a private Buenos Aires visible to the singer and few others, for reasons Bruno cannot immediately discern.

As the novel develops, Bruno learns that Martel’s invisible city stands in stark contrast to the city where guides take busloads of foreigners on tours with such titles as "Borges’s Buenos Aires." In effect, Martel’s impromptu performances are a unique form of street activism paying homage to individuals whose disappearance and death at the hands of the state and its representatives still remain unpunished. The sites he chooses to sing at—a street corner, a underground passageway beneath the Obelisk, the architectural wonder that is the Waterworks Palace—are closely tied to the crimes themselves.