In Iceland, a herd of horses is spooked by an unknown, loudly-breathing entity that makes its way to a barn. Later, farmer María and her husband Ingvar are shocked when one of their pregnant sheep gives birth to a human/sheep hybrid with a mostly human body and a lamb's head and right arm.
María and Ingvar take the hybrid infant in as their own and grow to love her as their own child, naming her Ada after María's deceased daughter. Ada's biological mother becomes a nuisance, attempting to contact Ada constantly and loitering outside the couple's home. Shortly after an incident where Ada goes missing and is later found next to the mother, María shoots Ada's mother and buries her body in a shallow, unmarked grave. Unbeknownst to her, Ingvar's brother Pétur, who arrives at the farmhouse shortly before the killing, witnesses the incident before sleeping in the barn.
Pétur, who makes sexual advances towards María, is very disturbed by Ada and maintains the belief that "it's an animal, not a child". Ingvar claims the whole situation has given them happiness. Increasingly angered and disturbed by María and Ingvar's attachment to Ada, Pétur takes her on an early morning walk while everyone is asleep with the intention of shooting her. After having a tearful change of heart, however, he is later seen soundly sleeping with Ada and soon becomes an uncle to her.
One evening, while María, Pétur, and Ingvar are having a drunken party, Ada witnesses the unknown entity from before near the barn. The entity then proceeds to kill the family's dog before taking the family's gun. After the party, a drunk Ingvar goes to bed. Pétur makes sexual advances towards María once again. When she rejects his advances, Pétur reveals that he witnessed María killing Ada's sheep mother, trying to blackmail María into having sex with him by threatening to reveal this to Ada. María pretends to be seduced by Pétur in order to lock him in a closet.
María drives him to the bus stop the next morning and sends him away, insisting she is committed to a new start with her family. After waking up to find María and Pétur missing, Ingvar takes Ada to fix a broken tractor. On their way back home, the entity, revealed to be a ram/man hybrid and Ada's biological father, emerges and shoots Ingvar in the neck, before taking a tearful Ada with him and walking away into the wilderness.
María returns home and finds that Ingvar and Ada are missing. She searches for the two and discovers Ingvar before he dies, and despairs at the loss of her husband and new child. María searches the wilderness in vain, before closing her tear-filled eyes.
