Macheath, a.k.a. Mac the Knife, "marries" Polly Peachum in a secret, unofficial ceremony. Her father, Jonathan Peachum, and mother, Celia Peachum, are not happy about losing their daughter. They are planning on using her as their retirement plan, and now she's gone and married a crook.
That's not to say that the Peachums are so sweet themselves; they run a ring of beggars that fake injuries and disabilities to inspire more pity and therefore get more jangle in their pockets. Mr. Peachum goes to the law, Chief Constable Jackie "Tiger" Brown, and reports Macheath's crime. It turns out, however, that Brown and Mac go way back, and while Mac is turned in by a prostitute and arrested, he easily escapes from jail.
Before he gets out of the slammer, though, Mac is visited not only by Polly, but also by his other best girl, Lucy. She fools him into believing she's pregnant, which could be a problem because her father is none other than Jackie Brown (the sheriff). The fight over Mac's heart goes nowhere, really, because as soon as he escapes he's betrayed once again by the prostitutes and sent to be hanged.
Right at the last minute, a royal official rides in with a pardon from the queen. He's also got a huge paycheck for Mac from the crown, just for kicks. Everyone else is still poor, and the bad guys have triumphed.