The play begins with the return of Sweeney Todd to London fifteen years after he, as Benjamin Barker, had been condemned to be transported to Australia for life. As a young man Barker had been a middle-class barber, married to a lovely wife, Lucy, and father of an infant daughter, Johanna. The lecherous Judge Turpin had wanted Lucy for himself, and had had her husband arrested and condemned on false charges. Todd declares that Barker is dead, but his lust for revenge is not.
The widow Mrs. Lovett runs a dismally unsuccessful meat pie shop on the ground floor of Todd’s old house. Mrs. Lovett recognizes her former neighbor, and tells him that Lucy, after being raped by Turpin, poisoned herself, and that the Judge had adopted baby Johanna as his ward. Johanna is now a young woman, in love with a sailor named Anthony, with whom she hopes to elope.
Adolfo Pirelli, a former assistant of Todd, also recognizes him and threatens to reveal his true identity – and if Todd should be exposed, he would hang – unless Pirelli is paid a handsome sum. Sweeney kills Pirelli, and Mrs. Lovett takes in the orphan boy, Toby Ragg, who was indentured to Pirelli. Yet Judge Turpin continues to escape Todd’s wrath. Todd then swears revenge upon the whole world, resolving to kill as many people as possible; Mrs. Lovett helpfully suggests that they turn the corpses of his victims into pies, and soon Mrs. Lovett's pie shop is doing a thriving business.
In the climactic scene, Todd finally manages to kill Judge Turpin, but at the same time takes the life of a deranged old beggar woman. The beggar woman turns out to be none other than Lucy Barker, Todd's long-lost wife. Mrs. Lovett confesses that it has been her love for Sweeney Todd, and her hopes that they would become lovers, that kept her from telling him Lucy was still alive. He throws Mrs. Lovett into the roaring hot pie oven.
Toby, realizing the secret of the meat pies, goes mad when he discovers Sweeney's murder of Mrs. Lovett – who was like a mother to him – and slashes Todd's throat with the barber’s own razor. Todd, having nothing to live for after his wife’s death, raises his head to expose his neck, and dies with Lucy’s body in his arms. Anthony and Johanna, who have witnessed the Judge's murder, return to the bakeshop with the police, only to find the floor littered with bodies. Toby, the only living soul left, is now a raving lunatic.
(Source: Masterworks Broadway site.)