Overview
Set in Victorian London, the play focuses on Macheath, an amoral, antiheroic criminal.

Macheath ("Mackie," or "Mack the Knife") marries Polly Peachum. This displeases her father, who controls the beggars of London, and he endeavours to have Macheath hanged. His attempts are hindered by the fact that the Chief of Police, Tiger Brown, is Macheath's old army comrade. Still, Peachum exerts his influence and eventually gets Macheath arrested and sentenced to hang. Macheath escapes this fate via a deus ex machina moments before the execution when, in an unrestrained parody of a happy ending, a messenger from the Queen arrives to pardon Macheath and grant him the title of Baron. The details of the original 1928 text have often been substantially modified in later productions.

A draft narration by Brecht for a concert performance begins: "You are about to hear an opera for beggars. Since this opera was intended to be as splendid as only beggars can imagine, and yet cheap enough for beggars to be able to watch, it is called the Threepenny Opera."

Prologue
A street singer entertains the crowd with the illustrated murder ballad or Bänkelsang, titled "Die Moritat von Mackie Messer" ("Ballad of Mack the Knife"). As the song concludes, a well-dressed man leaves the crowd and crosses the stage. This is Macheath, alias "Mack the Knife".

Act 1
The story begins in the shop of Jonathan Jeremiah Peachum, the boss of London's beggars, who outfits and trains the beggars in return for a slice of their takings from begging. In the first scene, the extent of Peachum's iniquity is immediately exposed. Filch, a new beggar, is obliged to bribe his way into the profession and agree to pay over to Peachum 50 percent of whatever he made; the previous day he had been severely beaten up for begging within the area of jurisdiction of Peachum's protection racket.

After finishing with the new man, Peachum becomes aware that his grown daughter Polly did not return home the previous night. Peachum, who sees his daughter as his own private property, concludes that she has become involved with Macheath. This does not suit Peachum at all, and he becomes determined to thwart this relationship and destroy Macheath.

The scene shifts to an empty stable where Macheath himself is preparing to marry Polly once his gang has stolen and brought all the necessary food and furnishings. No vows are exchanged, but Polly is satisfied, and everyone sits down to a banquet. Since none of the gang members can provide fitting entertainment, Polly gets up and sings "Seeräuberjenny", a revenge fantasy in which she is a scullery maid turning pirate queen to order the execution of her bosses and customers. The gang becomes nervous when the Chief of Police, Tiger Brown, arrives, but it's all part of the act; Brown had served with Mack in England's colonial wars and had intervened on numerous occasions to prevent the arrest of Macheath over the years. The old friends duet in the "Kanonen-Song" ("Cannon Song" or "Army Song"). In the next scene, Polly returns home and defiantly announces that she has married Macheath by singing the "Barbarasong" ("Barbara Song"). She stands fast against her parents' anger, but she inadvertently reveals Brown's connections to Macheath which they subsequently use to their advantage.

Act 2
Polly warns Macheath that her father will try to have him arrested. He is finally convinced that Peachum has enough influence to do it and makes arrangements to leave London, explaining the details of his bandit "business" to Polly so she can manage it in his absence. Before he leaves town, he stops at his favorite brothel, where he sees his ex-lover, Jenny. They sing the "Zuhälterballade" ("Pimp's Ballad", one of the Villon songs translated by Ammer) about their days together, but Macheath doesn't know Mrs Peachum has bribed Jenny to turn him in. Despite Brown's apologies, there's nothing he can do, and Macheath is dragged away to jail. After he sings the "Ballade vom angenehmen Leben" ("Ballad of the Pleasant Life"), another Villon/Ammer song, another girlfriend, Lucy (Brown's daughter) and Polly show up at the same time, setting the stage for a nasty argument that builds to the "Eifersuchtsduett" ("Jealousy Duet"). After Polly leaves, Lucy engineers Macheath's escape. When Mr Peachum finds out, he confronts Brown and threatens him, telling him that he will unleash all of his beggars during Queen Victoria's coronation parade, ruining the ceremony and costing Brown his job.

Act 3
Jenny comes to the Peachums' shop to demand her money for the betrayal of Macheath, which Mrs Peachum refuses to pay. Jenny reveals that Macheath is at Suky Tawdry's house. When Brown arrives, determined to arrest Peachum and the beggars, he is horrified to learn that the beggars are already in position and only Mr Peachum can stop them. To placate Peachum, Brown's only option is to arrest Macheath and have him executed. In the next scene, Macheath is back in jail and desperately trying to raise a sufficient bribe to get out again, even as the gallows are being assembled.

Soon it becomes clear that neither Polly nor the gang members can, or are willing to, raise any money, and Macheath prepares to die. He laments his fate and poses the 'Marxist' questions: "What's picking a lock compared to buying shares? What's breaking into a bank compared to founding one? What's murdering a man compared to employing one?" (These questions did not appear in the original version of the work, but first appeared in the musical Happy End, another Brecht/Weill/Hauptmann collaboration, in 1929 – they may in fact have been written not by Brecht, but by Hauptmann).

Macheath asks everyone for forgiveness ("Grave Inscription"). Then a sudden and intentionally comical reversal: Peachum announces that in this opera mercy will prevail over justice and that a messenger on horseback will arrive ("Walk to Gallows"); Brown arrives as that messenger and announces that Macheath has been pardoned by the queen and granted a title, a castle and a pension. The cast then sings the Finale, which ends with a plea that wrongdoing not be punished too harshly as life is harsh enough.