The first-person narrator is a pragmatic man living in an apartment in Mexico City. After a visit to the sea, he finds his life upended by a wave that follows him home. He attempts to manage the logistical and social complications of transporting his aquatic companion, a struggle that temporarily lands him in jail under accusations of poisoning the train's drinking fountain. Despite his initial reservations, he becomes deeply immersed in a passionate, though increasingly turbulent, relationship.

Personified as a tall, light woman with floating skirts, the wave impulsively leaves behind her vast ocean home to start a foreign life in Mexico City. She possesses immense physical and emotional power, bringing constant light and joy to the narrator's home early in their affair. Her nature is inherently restless, and she struggles with the confines of city living and the absence of her ocean community.

A school of fish brought into the home to provide the wave with a familiar connection to the sea. They quickly become the center of the wave's attention, swimming within her waters and adorning her hair. Their constant presence introduces severe tension into the household, as they command the affection that the narrator wishes to keep for himself.

An unnamed former romantic partner of the narrator who lives in the city. When the narrator begins to neglect his own life and becomes overwhelmed by his domestic situation, he turns to her for advice. She graciously listens to his secrets and attempts to offer support regarding his turbulent living situation.