How is revenge used in Sweeney Todd?

Sweeney Todd tells the story of Benjamin Barker, calling himself Todd, who exacts revenge on the corrupt Judge Turpin, the man who sent him to jail. Worse still, the judge raped Barker's wife, she died by suicide, and the judge adopted Barker's daughter, Johanna, now a teenager. It soon revealed that the judge plans to marry her.
Even as Barker is consumed by the idea of revenge, he turns his targets into literal victims of being consumed. As he starts on his vengeful path, unrelated people get in the way so he kills them too. Distracted from his chance to kill the judge while shaving him, he goes on a murder spree.
His landlady, Mrs. Lovett, is an eager accomplice, motivated by greed. She turns the victims' bodies into the meat for her delicious pie fillings, and sells them to unsuspecting customers.
One of the men Barker kills is Pirelli, a rival barber who tries to blackmail him after recognizing him as Barker. Trying to find his missing employer, Pirelli's assistant Tobias starts to get in the way so Mrs. Lovett locks him into her bakehouse. There he learns their grisly secret and escapes.
The play's resolution uses revenge to end the cycle of revenge. Barker learns that his wife had been alive, though mad, only when he kills her in her current state as a beggar. Intent on revenge, he had believed Mrs. Lovett's lies. He does manage to kill Judge Turpin, and then Mrs. Lovett too, but then Tobias immediately kills him--a full circle of vengeance.
Only his daughter Johanna and her true love Anthony escape the killings, but now she is an orphan.