My Last Dutchess is an example of Robert Browning's most successful style of poetry, the dramatic monologue. This is a poem in which only one person speaks, but the presence of another person is usually felt. In a dramatic monologue the narrator reveals a great deal about himself without any apparent intention of doing so. "My Last Duchess" was published in 1842; it is Browning’s best-known poem.

The narrator in "My Last Duchess" is partially based on Alfonso II, Duke of Ferrara, who lived in Italy during the 16th century. Thus we know the setting (geographical place and chronological time) of the poem.

The man listening to the duke is an agent (or representative) of a count whose daughter is going to be the duke's next wife. As the duke and the agent walk through the duke's home, the agent apparently comments on a painting of a woman with an interesting expression on her face; the duke says he is not the first to mention the joyous blush (lines 11-13). The duke explains that this was his last duchess. The painting was executed by Fra Pandolf, whose skill resulted in the duchess' looking as though she were alive. Obviously, she is now dead. The painting is covered by a curtain, which no one is permitted to open except the duke (9-10).

The duke proceeds to recount a list of his complaints about the former duchess. The duke criticizes his late wife for the lovely smile she bestowed on everyone (13-15), for her politeness to others (20-21), and for the pleasure she felt in the simplest of kindnesses shown to her. Examples are the innocent complements of the artist who painted her portrait (15-19), a beautiful sunset (24), the branch of cherry blossoms someone brought to her (27-28), and even the white mule she rode on the terrace (28-29). To the duke, these were among her shortcomings.

In addition to being equally pleasant to everyone, the late duchess failed to adequately recognize the worth of her husband (in his opinion). For example, she appreciated his 900 years old name no more than any other gift she received (32-34). Notice, however, that she was just as pleasant toward the duke as toward everyone else (43-45). The problem as the duke sees it is that she was no more pleasant to him than to others, and he feels she should have been. Her total reason for happiness should have been him.

The duke never shared his dissatisfaction with his wife although he is now willingly sharing it with the agent. (Perhaps he intends for the agent to share the do’s and don’t’s with the count’s daughter!) He says that to have told her she did not please him "would be some stooping; and I choose/Never to stoop" (42-43).

The duke shows no remorse or regret for having ordered his wife's death: " I gave commands;/then all smiles stopped together" (45-46). In fact, after having just revealed this ultimate domestic tyranny, he casually suggests that they continue down stairs to the meeting where the dowry the count's daughter will bring to her marriage is to be negotiated. Unconsciously the duke reveals his priorities: first his interest in the dowry (50-51) and second the count's "fair daughter's self" (52-53).

In the closing lines, rather than allow the agent to fail to notice another of the duke's prized possessions, he says, "Notice Neptune, though,/Taming a sea horse, thought a rarity" (54-55). Or perhaps the duke is suggesting that his future wife must be submissive (tame). . .or she will be tamed, as was the last (late) duchess!

Another opinion is that the Duke was engaged to this Counts daughter, and wanted to change his mind. In an effort to get out of the marriage without doing anything socially unseemly, he would just pretend that he is a mass murderer to this observer. So when the Count's agent comes over, he decides to give him a tour of his beautiful house. He goes on to tell the servant that he killed his last wife, when perhaps in reality she just left him for another. Well after the servant heard all of this he ran back to the Count and told him of these happening, and the marriage was broke off.

I personally don't go for this theory, because it would be more socially hazardous to be considered a murderer than someone who couldn't keep his wife from another man.

Either way, it's a nifty bit of writing.

Sources
http://www.students.dsu.edu/beversk/workshop/british_lit.htm
http://faculty.stcc.cc.tn.us/bmcclure/lessons2/browning.htm