A great answer! I would add just a few other instances of imagery which become part of the picture of that arrogant and haughty Duke.
The painting of his last Duchess is hanging on the wall, but it is apparently covered with a curtain, one that no one but him touches
"...(since none puts by
The curtain I have drawn for you, but I)..."
We have the sense of this huge paining, covered by a sumptuous curtain--likely heavy and rather difficult for a lesser man to maneuver--which no one ever opens except him.
He also, at the end of his humble little speech to the ambassador, points out another feature of this gallery.
"...Notice Neptune, though,
Taming a sea horse, thought a rarity,
Which Claus of Innsbruck cast in bronze for me!"
This final image, then, is both visual and tactile--a god taming some lesser creature , cast in unbending (heavy, unyielding) bronze. And it's made by, what else--a master. And it's just for him--no one else. It's hard to escape the correlation between this incredibly self-important, arrogant man and this statue.
When one thinks about appealing to readers' senses, one probably first thinks of imagery, since imagery, by definition, appeals to the senses. In Browning's "My Last Duchess," the speaker uses imagery to describe his former wife's portrait, as well as her looks and voice when she was alive.
According to the Duke, people have asked him what brought about the "glance" (visual imagery) seen on the wife's face in the portrait. And the glance is also referred to as a "spot of joy" (visual). In life, she used "approving speech" (auditory imagery), and at times she would "blush" (visual).
Imagery is also used to describe what gained his wife's approval and made her blush: "My favor at her breast," "The dropping of the daylight in the West," "bough of cherries," "the white mule/She rode with round the terrace."
The speaker is a hideous, arrogant, overly-proud human being, but, through imagery, he creates a beautiful vision of the wife he ordered killed, as well as that which caused her beauty to be heightened in her facial expressions and tender voice and words.