"My Last Duchess" by Robert Browning portrays only a limited subset of types of relationships between men and women. The poem is written in the form of a dramatic monologue, in which the Duke, a widower and the protagonist of the poem, is negotiating a marriage contract with the envoy of the father of the woman he plans to marry.
The Duke is what critics have termed a "collector" who discusses his dead wife in much the same artistic terms as he discusses his paintings and sculptures, with a tone that conveys both aesthetic appreciation and possessiveness. It is difficult to tell much about the character of the Duchess, given that we only see her through the eyes of the Duke. She may have flirted with other men, including the portrait painter, or may simply have been polite without any trace of impropriety. In discussing his second marriage, the Duke conveys a similar sense of treating it in a cool and businesslike fashion, as if he were acquiring a new work of art.
One could read the poem as a critique of the traditional marriage in which women were treated as property.