Marina Carr, the author of the play, has acknowledged that By the Bog of Cats was inspired by the myth of Medea. In Eurypides's theatrical adaptation, as in the ancient Greek myth, Medea is a sorceress and wife to the hero Jason. When her husband decides to marry another, she kills his new lover and their two children in revenge.
The main parallel between Medea and By the Bog of Cats is the way Hester Swane, the heroine, enacts her revenge on her disloyal husband, Carthage Kilbride. Her retaliation consists of setting fire to Carthage and his new wife's home and killing her own daughter, Josie, just as Medea punished Jason in the Greek myth. The significant difference between these two stories is the setting: while Medea is set in ancient Greece, By the Bog of Cats is transported to the bogs of Ireland.
A reviewer of the 2017 revival in Chicago noted that what makes the play distinct from Eurypides's adaptation, and what makes it distinctly Irish, is the themes of displacement and disposition. However, the heightened emotions and broad, existential themes of “love and hate, hope and despair, [and] grief and revenge” justify the comparisons of these two tragedies.