Sir Robert meets Mrs. Cheveley at his dinner party.
She threatens to expose the secret of Sir Robert's wealth – selling confidential info – if he doesn't publicly support a venture in which she has a vested interest. She has a letter incriminating him, and she'll happily show it to the press, ruining him forever.
Sir Robert tells her he will do as she asks.
Strong-armed by his wife, Sir Robert writes a letter to Mrs. Cheveley saying he will in fact not support the scheme.
The next morning, Sir Robert confesses everything to Lord Goring: he can't tell his wife about his past or she'll hate him; he can't cross Mrs. Cheveley or she'll ruin him. He doesn't know what to do.
Questioned by Lord Goring, Sir Robert confesses that he doesn't regret his past decision, which led directly to his current power and wealth.
Mrs. Cheveley beats Sir Robert back home and tells Lady Chiltern the truth about his past, leaving Sir Robert to explain himself.
In the face of a totally shocked, wounded and angry Lady Chiltern, Sir Robert explodes in a speech of self-defense. By putting him up on a pedestal, she's made it impossible for him to be honest with her.
That evening, Sir Robert discovers Mrs. Cheveley in Lord Goring's drawing room. He thinks his friend has been seduced and turned traitor.
The next morning, Sir Robert makes the speech Mrs. Cheveley doesn't want him to make. He tells Parliament that he cannot, in good faith, back the Argentine scheme – without knowing what the consequences will be.
When he gets home, he discovers that the damning letter has been burned. He has also found a letter from Lady Chiltern (originally addressed to Lord Goring) that he misconstrues as a love letter to him. He and Lady Chiltern make up.
Sir Robert offers to leave public office. Lady Chiltern says that it's a great idea.
Lord Caversham reports that Sir Robert is being offered a position in the Cabinet. Sir Robert is willing to turn it down; after all, he did promise his wife that he would leave politics. After a session with Lord Goring, Lady Chiltern changes her mind and urges her husband to accept the offer.
Things turn out well for Sir Robert. He doesn't have to publicly admit his youthful mistakes, he gets his wife back – and she's learned the lesson of forgiveness, too.
In the end, it seems that Lady Chiltern is willing to love Sir Robert as a real person, and not as an ideal husband.