What is the relationship between Jaime Lannister and Brienne of Tarth?

Jaime Lannister and Brienne of Tarth are characters from the popular television series Game of Thrones, based on the books by George R.R. Martin. The two characters have a complex and evolving relationship throughout the series, which spans eight seasons.

Initially, Jaime and Brienne are enemies, with Jaime being a member of the powerful Lannister family, and Brienne being a sworn sword of Renly Baratheon. However, over time, the two characters begin to develop a mutual respect and admiration for one another. This is particularly evident in the fourth season of the show, when Jaime and Brienne are traveling together, and Jaime reveals his reasons for killing the 'Mad King' Aerys Targaryen, earning Brienne's respect and understanding.

Despite this growing bond, Jaime and Brienne's relationship remains platonic for much of the series. However, in the eighth and final season, the two characters share a moment of intimacy, with Jaime sleeping with Brienne before ultimately leaving her to return to his sister Cersei.