A small party of pirates returns by dinghy to their ship, which is becalmed in the middle of the ocean. When they board the ship, their captain, Henry Avery, greets them. He notices that one of the men, McGrath, has a cut on his left hand. The captain says that the mate is a dead man, grabs his right hand, and reveals that there is a black spot on the palm. An unseen woman starts screaming and McGrath staggers across the deck toward the side. Avery and the others retreat to the captain's quarters and lock the door, and the captain wraps a mermaid medallion around the handle as a charm against "the Siren." They hear McGrath give a single scream and go out to investigate, and find nothing of him except his discarded gun.
Avery and his crew hear a banging noise from the cargo hold hatch and go to investigate. The Doctor pops out with Amy and Rory behind him, and the crew takes them to Avery's captain. The Doctor tries to explain that they picked up a distress signal and came to investigate, but Avery assumes that they're stowaways. He forces the Doctor to start walking the plank, warning that they have been becalmed for eight days and don't have enough food and water for three more people. They prepare to send Rory next and keep Amy as a serving wench since they figure she will use very little food and water. Rory complains that they're calling his wife a wench, but they toss Amy below. The Doctor tries to stall, asking Avery why he only has five crewmen left, and Amy finds a sword and coat and attacks Avery. They retreat from her in terror despite the fact she's clearly outnumbered, and she forces Avery to drop his gun. The captain warns her that she could get them all killed, and one of the pirates tries to grab her. Amy fights back and manages to injure one of the men, De Florres. A black spot appears on his hand, and Avery says that the Siren can smell blood, and rises out of the ocean to take injured men back with her. Another crewman crabs Amy and she slashes wildly, scratching Rory. A black spot appears on his hand as well.
The woman's son fills the air and Rory and De Florres become entrances, acting like fools. Avery explains that the Siren's song turns her victims into fools, making it impossible for them to resists. A woman surrounded in a blue glow rises from the water and lands on the deck, and De Florres eagerly runs to her. When he touches her extended hand, he explodes in a cloud of dust. When Amy holds Rory back, the Siren's glow turns red and she shrieks in anger. The Doctor grabs Rory and they retreat into the cargo hold, barring the door behind them.
Once they're safe, Avery explains that the Siren haunts that part of the ocean, attacking ships with treasure. He suggests that they leave in the TARDIS, the Doctor's "ship," and draws his gun to force the Doctor to take them away. Before the Doctor can decide, one of the crew realizes that there are leeches in the partially flooded hold. Everyone gets out the water but the bleeding crewman stares in horror as a black spot appears on her hand. The Doctor believes that they're safe locked in the hold, but the Siren emerges from the water and disintegrates the injured man. They retreat back to the deck, taking the entranced Rory with them despite his efforts to go to the Siren.
The Doctor deduces that the Siren can use any water as a portal, and Avery proposes that they lock themselves in the ship's magazine. When they go there, Avery realizes that someone has taken the key, but the door is unlocked. Inside they find a young boy, coughing and feverish, and Avery explains that it's his son, Toby. Toby tells his father that his mother always told him that Avery was a captain in the Navy, and that she died of typhoid fever. He came to join his father's crew and stowed away, and refuses to leave. Avery realizes that Toby has a black spot on his hand, and the Doctor concludes that any illness or injury attracts the Siren, which seeks out the weakest prey. The Doctor insists they go to the TARDIS, but Avery argues that he's the captain and should be making the decision. As they prepare to leave, Toby opens a barrel of water for a drink and the Siren's hand emerges. The Doctor hastily reseals the barrel and warns that any water, no matter how small, can provide a portal for the creature to pass through. The Doctor yields command to Avery to save time and asks what he wants to do. Avery gives his mermaid medallion to his son and takes the Doctor with him. They carefully make their way through the hold, avoiding any chance of injury, and enter the TARDIS.
Avery's Boatswain announces that he and the remaining crew are going to leave, abandoning Toby, Rory, and Amy. When Toby insists that they obey his father, saying he's a Naval officer, the Boatswain tells the boy that Avery is a pirate just like them, and has killed a thousand innocent men. He tells the remaining crew to grab all the treasure they can and head for the dinghy. Toby responds by grabbing a cutlass and telling the Boatswain to stay at his post. When he refuses, Toby scratches him with the cutlass and a black spot appears on the man's hand. The boatswain prepares to shoot Toby, but Rory warns him against setting off a spark in the magazine and blowing them all up. The other uninjured pirates, led by Mulligan, take the Boatswain's key and leave him.
The Doctor tries to pilot the TARDIS away from the pirate ship, but discover that the vehicle is unable to lock onto the time/space vortex. Tremors shake the TARDIS and the Doctor discovers that the controls are jammed. He tells Avery that the vessel is having a tantrum, grabs the captain, and gets them both out of the TARDIS just as it dematerializes. They head for the magazine and come face-to-face with Mulligan, loaded down with treasure. He holds them off with a gun and gets around them. He follows after them but he unlocks a door using the Boatswain's key, goes inside into the dark, and bars the door behind him. When he tries to strike a light, he scratches himself. Outside, the Doctor and Avery hear the Siren's song and then Mulligan's scream. The Doctor gets the door open but the room is dry and there's no sign of Mulligan. When they spot the jeweled crown that Mulligan was carrying, the Doctor tells Avery to forget his previous theory: the Siren is using reflections, not water, to travel through the ship and kill her prey. It goes after ships with treasure because the gold and silver are highly reflective, and they go back to warn the others.
In the magazine, Toby polishes his father's silver mermaid medallion. The Doctor and Avery barge in and the Doctor breaths on the medallion, blurring its surface before the Siren can appear. He orders Avery to get rid of all of the treasure while he starts breaking every reflective glass surface. When Avery hesitates, the Doctor tells him that the Siren will get Toby if he don't get ditch the treasure.
After smashing all of the glass, the Doctor tells Amy and Rory that they will have to wait until the wind picks up, and that they can't go on the deck because the still surface of the ocean allows the Siren to appear. They seal themselves in below decks and try to sleep. Avery apologizes to Toby for abandoning his wife and son, and Toby says that his mother waited three years for Avery to return as he promises. He asks Avery why he became a pirate, but his father refuses to answer. Meanwhile dreams of the eye patch woman appearing to her through a hole in the side of the hull. The woman says that Amy is doing fine and tells her to stay calm, and then seals the hole. Startled, Amy wakes up but isn't sure if what she saw was real or part of her dream.
The Doctor goes out on the deck and Avery joins him as the Time Lord looks up at the stars and talks about how lonely it is to travel without a companion. Avery admits that he'll take Toby back to England if they escape the Siren, but he won't take him on his travels. The Doctor asks what Avery is, a rogue or a Naval officer, and Avery says that his course is set and he can't change it. However, the Doctor says that things can change when someone least expects them.
Amy finds the Doctor in the captain's quarters, and he says that he can feel someone watching them. A storm starts up and they go to the deck to rig the sailing. The Doctor takes the wheel while Avery directs Rory and Amy. Toby brings his father his coat, but the crown falls out and rolls across the date. The Siren emerges from the reflective surface and disintegrates Toby, and then disappears as the Doctor throws the crown overboard. The Time Lord angrily turns on Avery, blaming him for dooming his son and ruining his career as an officer by choosing treasure instead.
A swinging mast knocks Rory into the ocean, and the Doctor stops Amy from diving in, warning that she'll drown. He tells her that they have no choice but to summon the Siren and hope they can appeal to it as an intelligent creature to rescue Rory rather than kill him. The Doctor opens a barrel of water and the Siren appears, and he asks it to find Rory. It dives into the water after Rory, and the Doctor speculates that since it is an intelligent creature, it did something other than kill the other crew as well. He suggests that they all three prick their fingers to attract the Siren, and Amy and Avery reluctantly agree. When the prick their fingers, black spots appear on their hands and the Siren returns and touches all of them.
The Doctor, Amy, and Avery find themselves lying on the floor of a room in a spaceship. A viewport in the wall shows the deck of the pirate ship, and the Doctor realizes that they are trapped in a temporal rift, occupying the same space as the pirate ship but in an adjacent plane of existence. Reflections act as portals between the two worlds, letting the Siren travel back and forth between the two realities. The Doctor tosses a piece of metal through the portal and it lands on the deck of the pirate ship, confirming his theory. An alarm goes off and they realize it is the distress signal that the TARIDS homed in on. They explore the ship and find a control room with two dead alien crewmen. They have a portal that looks into Avery's quarters, and the Doctor realizes the corpses were what were "staring" at him earlier. The Doctor concludes that the aliens died of bacteria that leaked through the mirror interfaces, and that the Siren was a stowaway.
Investigating further, the Doctor, Amy, and Avery find a room with the pirate crew on tables, hooked up to life support equipment and kept unconscious. Toby and Rory are there, and the TARDIS is back behind one wall. The Doctor concludes that the black spots are really tissue samples. He starts to revive Rory, but they hide when they hear the siren coming. She enters the chamber and puts Rory back to sleep using her song. When the Siren approaches Toby, Avery shoots it but the bullet has no effect. She transforms into its demonic form and advances on it, but then turns to the Doctor when he sneezes. The creature causes a glowing fireball to appear between its hands as it advances, and the Doctor sneezes into a handkerchief and throws it on the floor. The Siren incinerates it and then turns back to Rory as Amy tries to revive her husband. The Doctor quickly explains that the Siren is an automated medical program that served the stranded alien crew. When it failed to save them, it "adopted" the human crew of the pirate ship and took on human form to avoid frightening them.
Avery and Amy try to free Toby and Rory, respectively, but the Siren drives them back. The Doctor tells Amy to show her wedding ring and prove that she can sign a consent form to approach Rory and release the Siren from its perceived obligation. Amy tearfully tells the Siren that she is Rory's wife, and it creates a glowing circle of life. The Doctor explains that it's the consent form and tells Amy to put her hand through it. She does so and the Siren disappears, allowing Amy to shut down Rory's life support systems. However, he starts choking and Amy turns the system back on. The Doctor explains that the Siren saved Rory as he was drowning, but lacks the knowledge of human anatomy to save him. Rory tells Amy to show the Siren how to use CPR to resuscitate him. When she hesitates, Rory insists that she can do it and that he knows she'll never give up.
Meanwhile, the Doctor tells Avery that they have to release the spaceship. Avery asks about his son and the Doctor admits that the Siren can't cure Toby of typhoid fever. The Siren can sustain him aboard the ship but it can't cure the boy. Avery offers to stay with his son and pilot the spaceship away from Earth, since he no longer has a home in England. The Doctor checks on Rory and Amy, and they prepare to release him. When Rory is released from the life support system, he starts to drown again. The Doctor and Amy get him into the TARDIS, and Amy administers CPR. After a long struggle, she manages to revive him.
Later, Avery pilots the spaceship away from earth with Toby at his side, and the rest of his crew behind him.
The Doctor pilots the TARDIS away from Earth, and he admits to Amy that he always worries about her. When they're alone, Rory warns Amy that she can't tell the Doctor what they know of the future where he'll be killed. Amy admits that he's right and they leave. Meanwhile, the Doctor checks the TARDIS scanner, which continues to show that Amy is simultaneously pregnant and not pregnant at the same time.