Drama; Modernism; Satire and Parody
Okay, so let's start with the easy one: drama. The Threepenny Opera is a drama because it's written for theatrical performance, and all of the story and relationships are expressed through dialogue and onstage action rather than descriptive prose. Got it? Good.
Brecht is considered a modernist in the literary sense (In fact, he's even listed in our very own definition of modernism.) Modernism is a literary movement that was all about stirring things up, finding ways to present various perspectives at once. For Brecht, the theatre's various elements of light, music, sound, costume, and gesture, all allowed for different, modern combinations.
One of the most important innovations in Brecht's modern drama (he called it "epic theatre") is the defamiliarization effect, where he forced audiences to recognize that they were seeing a play and not get caught up in the drama. The signs that are held up in between scenes, the music, and the direct address to the audience are all part of Brecht's modernist project.
Brecht used the defamiliarization effect in order to criticize human problems like greed, dishonesty, and hypocrisy. In many cases these vices are so exaggerated that it's absurd and even funny, which lands the play smack in the satire and parody categories.