The film takes place during an unspecified number of months after the Munich Massacre in West Germany. Emmi, a 60-year-old window cleaner and widow, enters a bar, driven in by the rain and wanting to listen to the music being played inside. The barmaid goads Ali, a Moroccan Gastarbeiter or guest worker in his late thirties, to ask Emmi to dance. She accepts. They develop a friendship and Ali ends up staying overnight at Emmi's apartment. After more interaction, their connection deepens and Ali moves in. Eager to share her happiness, Emmi introduces Ali to her children: Krista and her domineering husband, Eugen. Eugen scoffs, convinced Emmi has lost her mind, while Krista dismisses it as a fantasy fueled by years of widowhood.
Their relationship is threatened when the landlord's son, who has been sent on the assumption that Emmi has taken in a lodger, tells Emmi that subletting is against Emmi's tenancy agreement, and that Ali must leave within a day. Fearful of losing Ali, Emmi claims that she and Ali are planning to marry. After the landlord's son apologises for the misapprehension and leaves, Emmi speaks to Ali and apologises for having invented the idea of her marrying him, but is surprised by Ali when he says that it is an excellent idea. The film then shows them in a civil court, married.
Their marriage is looked upon negatively by those who live near them, which include apartment tenants and shopkeepers. Emmi is shunned by her colleagues, and Ali faces discrimination at every turn. When Emmi invites her three grown children and son-in-law to meet Ali, they openly reject him. One of Emmi's sons smashes her TV set in anger, her other son declares she must have lost her mind, calling her a "whore". Before they leave Emmi's apartment, her daughter describes it as a "pigsty".
Emmi's sadness towards this rejection washes away as her optimism resurfaces and she decides that she and Ali should take a long holiday together to escape the discrimination, convinced that upon their return, they will have been missed and will be welcomed back. After their return, they face less discrimination, but only because neighbouring tenants and shopkeepers see the gain in treating Emmi better, not because they have outgrown their prejudices.
Wanting to get back with her old friends after their apparent renewed respect, Emmi begins to neglect Ali and adopt some of their attitudes toward him. She becomes more strict, ordering him to do more things. When co-workers visit and remark on how surprisingly clean he is and comment on his muscles, she shows him off as if he were an object. This causes Ali to leave, to which Emmi remarks to her friends of his "mood swings" and that his attitude must be due to his "foreigner mentality". Ali seeks comfort in bar maid Barbara, who it is suggested he had a relationship with prior to meeting Emmi. Ali returns to Barbara on another day, spending the night with her. Emmi visits Ali at work, where he pretends he doesn't know her; his workmates make fun of her age, calling her his "Moroccan grandmother", to which Ali does not intervene.
When it seems as if the relationship is beyond repair, Emmi goes back to the bar where they first met to meet with Ali. She has the barmaid play the same song on the jukebox that led to their dance at the beginning of the film. Dancing together, Emmi emphasizes that she knows she is old and that he is free to come and go. However, when they are together, they must be kind to each other. Ali agrees and they declare their love. After collapsing in Emmi's arms from a burst stomach ulcer, Ali is taken to the hospital with Emmi at his side. A doctor tells her the illness is common among foreign workers because of the stress they face in everyday life. He explains that Ali will undergo surgery to remove the ulcer, but will probably be back in six months with a new lesion. Emmi declares that she will do everything in her power to prevent this from happening. The film ends with her holding Ali's hand.
