Eliza Cooper was an agent of the Torchwood Institute.
In 1906, Eliza and Robert went through a time machine. They were transported to a different planet thousands of years in the future. There they encountered the Doctor. They tried to arrest him. Eliza however, soon realised that they needed the Doctor to return home. She was ready to trust him, having seen his heroics in their files and heard Jack Harkness speak about him.