Sam Dawson (Sean Penn), a mentally challenged man with a mind of a child, is living in Los Angeles and is single-handedly raising his daughter Lucy (Dakota Fanning), whom he fathered from a homeless woman who wanted nothing to do with Lucy and left him the day of her birth. Although Sam provides a loving and caring environment for the 7-year-old Lucy, she soon surpasses her father's mental capacity. Questions arise about Sams ability to care for Lucy and a custody case is brought to court.Sam is a man with a mental age of 7 who is well adjusted and has a great support system consisting of four similarly developmentally disabled men. His neighbor Annie (Dianne Wiest), a piano-player and agoraphobe, befriends Sam and takes care of Lucy when Sam can't.Sam works at Starbucks bussing tables. Sam is popular with the customers, whom he addresses by name and favorite coffee. His job gets difficult when Lucy starts grabbing objects, making a woman spill iced coffee down her shirt. In a humorous, but innocent exchange, Sam tries to remove an ice cube from the startled woman's cleavage. Sam then brings Lucy to his neighbor and baby Lucy croons, "Annie!" Sam says, "Her first word was Annie." Flustered but flattered, she retorts, "And people worry you aren't smart," and agrees to function as Lucy's babysitter.Lucy is as precocious as Sam is backwards. Sam loves reading Green Eggs and Ham by Dr. Seuss to her, but when she starts reading "real hard" books like Stellaluna, she balks at reading the word "different" because she doesn't want to be smarter than her dad. She knows he's different, "not like other dads", but that's all right with her because he is loving, taking her to the park and to International House of Pancakes (every Wednesday, because "Wednesday is IHOP night").When they decide to go to Big Boy for a change, Sam causes a disturbance because he cannot get the kind of French pancakes he is accustomed to. At the school Halloween party, he dresses as Paul McCartney but embarrasses his daughter by drawing undue attention. Other kids tease her, calling her dad a "retard". She tells one boy that she is adopted. This causes a crisis at her birthday party, which results in an unexpected visit from a social worker who takes Lucy away. A judge allows him only two supervised, 2-hour visits per week.Sam's friends recommend that he hire Rita (Michelle Pfeiffer), a lawyer. He shows up at her office and starts spelling out his situation while she juggles coffee orders to her assistant, Patricia. Socially, Sam is rather high-functioningmore together in many ways than his high-class, respected lawyer whose marriage is falling apart and whose son hates her.Sam surprises Rita at a party. Stunned, she announces that she's taking his case pro bono, because others see her as cold and heartless.Rita begrudgingly works with Sam to help him keep his parental rights, but chaos arises when Lucy convinces Sam to help her run away from the foster home she is being kept in during the trial. Over the course of the trial, Sam gets a new job at Pizza Hut and Annie leaves her apartment for the first time in years. Sam also helps Rita with her family problems, and helps her to realize how much her son really means to her. Sam also convinces her to leave her husband, because Rita told him that he cheated on her.During the trial, however, Sam breaks down, after being convinced that he is not capable of taking care of Lucy.Meanwhile, Lucy is placed with a foster family who plan to adopt her. Lucy often runs away from her foster parents in the middle of the night to go see Sam, who moved into a larger apartment closer to her.In the end, the foster family who planned on adopting Lucy lets Sam have custody of her. Sam says that Lucy still needs a mother and asks if the foster mother would like to help raise Lucy. The movie ends with Lucy's soccer game where Sam is the referee. In attendance are Lucy's former foster family, the newly divorced Rita and her son with whom Rita has renewed her relationship, along with Annie and Sam's other friends.