Swallow the Air’s narrative takes place in a series of vignettes. In the first, May, the protagonist, recollects her memories of her mother’s suicide. Mum tells May and her older brother, Billy, to go fishing and to return to Aunty’s house when it gets dark. The children race down to the ocean, where May spots a dead stingray. Neither child catches much, and when they arrive at Aunty’s house they see a police car in front; they run inside and find Aunty crying. She tells them that their mother is gone forever.
Next, May describes Aunty’s descent into gambling. One day, she wins a raffle at the local supermarket and gets to take home cartloads of free groceries. Aunty is elated by the prospect of feeding May and Billy a real Christmas turkey for the first time. In hopes of paying off their many bills, she starts playing the lottery and eventually becomes addicted to poker. As her losses pile up, Aunty becomes addicted to alcohol as well.
In their free time, May and Billy go “cloud busting” at the beach, where they look at the sky, explore the dunes, and collect shells and sometimes small fish. When she was alive, Mum used to fry the fish in her own mother’s saucepan, which always reminded her of the same story. As a child, Mum lived in a dismal government housing project with her mother Alice. One day, a white traveling salesman arrives and shows all the women in the complex the beautiful cookware he’s selling. All the women laugh, since they can’t afford any of it, but Alice is enraptured and agrees to pay for the pans in installments. Over three years, while she saves up the money, she befriends the salesman, Samuel; when she finally pays for the pans, Samuel brings packages of meat and food along with them. Now, the pots belong to Mum and she uses them to cook for her children.
Now, May is eighth grade. Although her family is poor and Aunty is still gambling, she feels content, since she’s won an art prize at school and Billy has a coveted job delivering milk. One day May goes walking on the beach. Once she was familiar with this part of town, but now it’s popular with surfers who are racist and hostile towards people like her. May sees a fistfight ahead of her and tries to hide. However, one of the men sees her and pursues her through the sand until he catches her. Drawing a knife on May and calling her a “dumb black bitch,” he rapes her and then leaves.
When May is fourteen, she receives a postcard from her long-absent father, apologizing for having been out of contact so long and telling her that he’s been living near Darwin and picking mangoes. May looks at the postcard’s idyllic description of a mango tree and imagines her Dad living in this perfect world. She remembers how he taught her to fish when she was a child. Her memories are so strong that it seems like he never left. Billy has a different father. Unlike May’s father, Billy’s father was Australian Aboriginal; because Billy had a heart condition and required a lot of care, he left Mum to join a band and eventually committed suicide. Billy was a sickly baby and learned to walk late, but once he did he hated to sit down, convincing Mum that he’s a “fighter.”
When Billy turns eighteen, Aunty gives him a flask of liquor. Billy invites May to see Terminator with him and a friend, and she’s delighted to be included. However, when they get home, they find Aunty’s abusive boyfriend, Craig, pushing her face toward the hot stove. Billy leaps on Craig, but Craig punches him in the chest and Billy falls to the floor. Watching him gasp for breath, May worries that his fragile heart will fail. After a few moments Billy gets up and walks out of the house, saying he’s leaving for good. Although she knows all his usual hiding places, May can’t track him down.
Shortly after Billy runs away, May decides to leave and look for her father, whom she imagines can’t be a worse caretaker than Aunty. First, she goes to a squat where one of her friends once lived. Its inhabitants welcome her in and introduce her to “poppies,” an addictive drink made of opium. After grocery shopping one day, May finds that Billy has arrived in the squat in the company of several heroin addicts. He’s happy to see her, but she’s worried because he’s clearly been using drugs. That night, May goes to the bathroom and finds the dead body of a girl who has overdosed. The others abandon her body at a nearby train station and May, horrified, leaves the squat.
May hitches a ride with a friendly trucker heading towards Darwin. On the way, they stop at a rodeo, where May witnesses a brutal prizefight. She surveys the men who are watching the violence and realizes that one of them is her father. Seeing him in this context forces her to remember not just good times but also his constant abuse of Mum. She decides not to go looking for him in Darwin.
Instead, May reaches Sydney and lives on the streets. One night, an old Aboriginal woman named Joyce finds her and takes her home. Her house is small, decrepit, and located in a poor neighborhood, but Joyce is proud of her large family. May moves in with her, her daughter Justine, and Justine’s son Johnny. She loves the warm atmosphere of the house, where the women sit up all night smoking and telling stories. Joyce talks about her family and encourages May to learn about her own people.
While she lives in Sydney, May works at a carwash with an African immigrant named. They both dislike their tyrannical and racist boss, Mr. Tzuilakis. Neither Charlie nor May share their backgrounds, but they become good friends. May even starts to think of him as a father figure. One day, the police arrive and deport Charlie; it’s clear that Mr. Tzuilakis has turned in his own worker. Later that day, some boys from the neighborhood sneak into the chemical room to steal. Thinking that May has let them in, Mr. Tzuilakis fires her and calls the police, who come to Joyce’s house. It’s only because of Joyce’s furious defense that May doesn’t get arrested.
May’s best friend is Johnny, who’s about her age. In their free time, they walk the city and talk about the traditional lands of their tribes, even though neither has ever been there. In their daydreams, they paddle around their islands in canoes, dance to traditional music, and sleep in cabins under tropical storms. Johnny reminds May of her brother.
One day, May is arrested for staying with some friends in a squat, and she spends the night in jail. In the morning, she realizes she needs to leave this grim city behind. She finds Johnny and tells him they should leave to look for their families in the country. Johnny refuses to come, saying their daydreams were just fantasies. Enraged, May tells him he’s a “nobody” with no ambitions, and storms out of the house.
May hitches a ride to Lake Cowal with another trucker, who tells her that a mining compound has recently set up operations in the town she’s looking for. When May arrives, she sees their compound bordered by a barbed wire fence. She remembers Mum’s stories, which always centered around this place, the land of their ancestors.
In the town, May meets an Aboriginal elder named Issy, who is leading protests against the mining company. She says that while the mining corporation sees the land as empty and useless, the Aborigines whose people once lived here have a deep connection to the land. In a flashback, May remembers sitting around a fire as Mum told stories and Billy tended the fire. May remembers these as the best times in her life.
Issy instructs May that in order to find the remains of her tribe, she should walk along the river for four days. As she walks, surviving on fish she catches in the river, May tries not to worry about what she’ll find. Eventually, she reaches the road and walks towards Eubalong, the town where her relatives live.
May hitchhikes to a mission outside Eubalong. She meets an old man sitting on his front porch, and tells him she’s looking for the Gibsons. He tells her that the inhabitants of the mission have become alcoholics because of their bleak prospects and discrimination by the government, which is still trying to “kill off us fellows.” He directs her to an old woman, Betty, who knows more about families living in the area. Betty’s daughter, Jo, agrees to drive May to Lake Cargelligo, where the only Gibsons she knows live.
May finds herself at a neat white house and knocks on the door. Inside, she finds her distant cousin, Percy Gibson. He asks her skeptically if shes wants money, and laughs at her when she says she’s looking for “stories.” He tells her she’s just like her grandmother, who left the town “looking for…meaning” and returned destitute with several children. Percy says that when he was growing up, people “weren’t allowed to be Aboriginal,” so the old stories don’t exist anymore.
Percy leaves to play golf, but his wife Dotty feeds May before she sets out again. At first, May is crushed by her cousin’s behavior, but as she walks down the highway she has an epiphany and realizes that “this land is belonging, all of it for all of us.” Her new connection to the environment makes her feel closer to her mother.
May finds another trucker to give her a ride away from the town. Before leaving she buys some food in a supermarket and sees in a newspaper that Johnny has been killed in a police chase. While she’s devastated, she’s also happy that he died with his dreams intact, having never chosen to test them.
In a flashback, May remembers the jacaranda tree that stood in the backyard of Mum’s house. It bloomed briefly each year, and Mum always threatened to chop it down but secretly loved it. When Mum finally committed suicide, her body was found under the jacaranda tree, and May finds peace in imagining her lying there.
When May returns to her town, she imagines that Mum knows she’s there. She also knows that she has to stop running away and embrace what remains of her family. May arrives at Aunty’s house only to find her aunt crying at the kitchen table. Aunty informs her that they’re being evicted. However, May is delighted to see that Billy is there and that he’s not using drugs. May knows that one of Aunty’s few pleasures is buying a new tablecloth for her kitchen table; as a child, she always visited Aunty’s house to celebrate one of these purchases. To cheer Aunty up, she suggests that they go the store and buy a new tablecloth. Aunty agrees, excited.
Outside, May sees gulls drifting over the ocean and hears an excavator starting in the distance. She wonders what it would take to stop them from digging up Aunty’s backyard, “digging up a mother’s memory…digging up our people.”