In Robert Browning's dramatic monologue "My Last Duchess," the Duchess meets an untimely end. Most readers infer that she was murdered by the Duke, but Browning himself answered the repeated questions he received about the Duchess' fate by suggesting she had been sent to a monastery. That reply may have been facetious, however. Let's assume for purposes of this question that she was murdered by the Duke as indicated by his statement, "I gave commands. Then all smiles stopped together."
Did the Duchess do anything worthy of capital punishment? Certainly not from what we can tell. We infer from what the Duke tells the Count's messenger, the one he is speaking to, that the Duchess was expressive, kind, and innocent. She thanked people who gave her little gifts, she smiled at people who passed her, and she enjoyed the simple pleasures available to her, like watching a sunset or riding a white mule around the terrace. When the artist painting her portrait made comments about her physical appearance, she blushed, and she blushed at other pleasures or comments, showing she may have been shy and self-conscious. The "crime" that the Duke believes she committed was that she did not offer the type of obsequious gratitude to him that he felt he deserved for having made her Duchess.
Now, consider the Duke. He was jealous of anything or anyone the Duchess looked at, spoke to, or blushed at. He was jealous that the way she thanked others was similar to the way she thanked him. He was too proud to let her know of things that she did that disgusted him or missed the mark. He felt communicating with her as an equal would be stooping. Rather than stoop to let her know what he wanted and expected--or rather than trying to change his own feelings and attitudes, which would have been better, he killed his wife. In this poem, there is no question that the Duke is the guilty party and the Duchess was completely innocent.