Concerning Browning's "My Last Duchess," I'll cover theme in the poem for you and let another editor deal with dramatic irony and repetition.
The enotes Study Guide on the poem lists two prominent themes: Pride, and Art and Experience.
The speaker of the poem is conspicuously proud of his artwork. He begins and ends the poem showing works of art to his silent listener. The art is valuable even more for its reflection on the speaker, than for any artistic value. The duke wants to show off his good taste. He is excessively proud of his heritage, as well. He is so prideful he refuses to "stoop," as he calls it, and the price for making him even contemplate doing so is death.
The problem is also that the speaker thinks of people the same way he thinks of his art. This reveals the second theme: Art and experience. He is much happier now that his wife is reduced to a work of art, which of course, figuratively speaking, obeys absolutely. His wife would not behave like one of his works of art, so he destroys her.
Implied is the necessity for his new possession, his new bride-to-be, to grant the duke absolute authority and behave like a work of art.