Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Exposition
Bad Stuff
The initial situation is pretty grim. Vindice wants revenge for the murder of his fiancée nine years ago, when the Duke poisoned her because she wouldn't sleep with him. Antonio wants revenge because the Duchess's son Junior raped his wife, and she committed suicide because of the rape. It's hard to get much grimmer for a starting scenario.
It's in this dark situation that Vindice's brother Hippolito manages to smuggle Vindice into the court, disguised as a bad guy who will help Lussurioso, the Duke's son, do his dirty work. Vindice is hoping for an opportunity for revenge against the Duke, while Lussurioso wants someone to act as a go-between as he tries to seduce a woman.
Rising Action
The Plot Thickens
And boy, does it ever. It turns out the woman Lussurioso wants to seduce is Vindice's sister, so now Vindice and Hippolito want revenge against Lussurioso, too. Vindice puts himself in complicated ethical and familial territory by pleading Lussurioso's cause to his sister Castiza, hoping all the time that she'll say no. Castiza turns the offer down, but her mother thinks it's not such a bad idea, since she's poor and wants the money Lussurioso will give Castiza if she sleeps with him. This causes family complications—surprise, surprise.
In case things weren't messy enough, the members of the Duke's family are scheming against each other (and everybody else) in all sorts of ways. The Duchess wants revenge on the Duke for not immediately letting her son Junior off for the rape, so she starts an affair with the Duke's illegitimate son, Spurio, who incidentally wants all his family out of the way so that he can gain power. The Duchess's three sons from a previous marriage are scheming for a bunch of things—trying to get Junior out of prison, trying to get Lussurioso killed, you name it.
Complication is definitely the right word for what happens in this plot. This scheming just keeps on going.
Climax
Revenge, Served Cold
In Act 3, earlier than usual, we reach the moment the whole plot has been building to: Vindice gets a chance to kill the Duke, and he takes it—the Duke never sees it coming. It takes a while for the news to get out, but when it does, it causes even more scheming.
Lussurioso is supposed to inherit the Dukedom, but naturally his half brother and stepbrothers want in on the act (except the one who accidentally got killed in all the earlier scheming). Somewhere in there, Vindice, Hippolito, and Castiza manage to bring their mother around to supporting Castiza's choice to remain chaste, so at least the Vindice family is at peace with each other.
As we head into the major party that kicks off Lussurioso's time as Duke, Vindice and pals are planning to do Lussurioso in during the party, while his brothers are next in line to get him if Vindice fails. It all feels like a Mafia thriller.
Falling Action
Rocks Fall, Everyone Dies
Pretty much everyone, anyhow. Vindice stabs Lussurioso during a dance number (we are not kidding), and when Lussurioso's brothers, who are in charge of the next dance number, discover that he's dead, they instantly start claiming the title and killing each other off. They're all dead by the end, so the title of Duke passes to good old Antonio, who seems like a decent fellow for the most part.
Resolution
Breaking Bad
Vindice and Hippolito figure it's safe to admit they killed the old duke now, so they tell Antonio. Antonio is deeply shocked, and says they're likely to murder him, too, so he condemns them to execution. They complain a bit, but take it pretty well, considering. They've gotten their revenge, and their mother and sister are back on the same team, so they figure it's not that terrible.
Antonio ends the play with a lament for the times and a wish that things will improve. We have to say it seems pretty likely. After all, how could they get much worse? Welcome to revenge tragedy.