A landmark of 21st-century TV drama is about to finish its 10-year run. Its star reflects on how playing Carrie Mathison – and learning from real spies – has shaped her view of politics

Perhaps the defining image of Homeland, one of the most ambitious US drama series of the past decade, is Claire Danes’s character, Carrie Mathison, a mercurial CIA officer, staring at a video screen and displaying a sixth sense for the vital clue. So it is fitting that Danes appears to this interviewer not in person but via FaceTime.

“Let me just get on to my wifi,” she says, as the signal flickers, “I thought I was. OK, that should be better.”