But apparently the romance continues off-screen as well.
Catherine Hardwicke, director of the first film, reveals that the non-stop speculation surrounding the stars' love affair isn't without reason.
"In terms of what Kristen told me directly, it didn't happen on the first movie. Nothing crossed the line while on the first film," she tells Time magazine.
"I think it took a long time for Kristen to realize, 'OK, I've got to give this a go and really try to be with this person,'" she adds.
Meanwhile, Kristen and Rob - who are currently criss-crossing the globe to promote the second film in the vampire saga, New Moon - continue to leave fans guessing.
At an event in London on Wednesday, Kristen said she's on "Team Jake," supporting Bella's relationship with Taylor Lautner's character.
"If I was friends with Bella I'd be like: 'Please make life easier and date Jacob'," she said.
Kristen, Rob and Taylor spent some time with fans in Madrid on Thursday before heading to Germany.