Robert Browning's "My Last Duchess" is a dramatic monologue set ion much the same imaginary construction of Renaissance Italy as that of Jacobean revenge tragedy. Within this setting, marriage was primarily an economic arrangement, rather than having the sort of romantic expectations of the Brownings' own marriage. The Duke negotiates for a new bride in straightforwardly economic terms:
The Count your master's known munificence
Is ample warrant that no just pretence
Of mine for dowry will be disallowed;
He is also often described as a collector of beautiful objects, and as well as seeing women as part of an economic system, also views them in terms of aesthetic exteriors, just as he views his art works. He is possessive of both.
The duke primarily views women as beautiful objects to be possessed by their husbands. In fact, he is so possessive and feels so entitled to his last duchess that he says to his auditor, "none puts by / The curtain I have drawn for you, but I." He keeps the portrait of his dead wife behind a curtain so as to hide her from anyone except those with whom he chooses to share her. He determines who gets to see and enjoy her, and to him, this is the way it should be. Further, he treats her portrait as just another possession, as he finishes the poem by saying, "Notice Neptune, though, / Taming a sea-horse, thought a rarity, / Which Claus of Innsbruck cast in bronze for me!" Her portrait is only one more beautiful thing that he owns, just like the sculpture of the god of the sea, a sculpture with which he seems to have as much emotional connection as he does with the painting of his dead wife.
In fact, it was his last duchess's unwillingness to save all her smiles and blushes just for him that caused him to "[give] commands; / Then all smiles stopped together." It sounds as though, displeased with her uniform pleasure and gratitude whether a gift were small (like a branch of flowers) or large (like his status and important name), he had her killed so that he could start over with a new wife who would allow herself to be possessed by him completely. During her life, he was unable to possess her, and so he reduced her to a portrait that only he is allowed to control. The duke expresses no remorse or sadness that she is gone, because he feels none; he only feels pride in the possession of her lovely portrait because he can truly possess it in a way that he could never possess her when she was alive.