Scarlett Johansson wasn't fazed when she was asked to play the voice of a futuristic computer operating system who falls in love with a human in Her. She wasn't even intimidated by a cybersex scene, though "to think my dad is going to watch is awful," she admits. What does terrify her is the very non-science fiction notion of online dating. "Just the thought of building a profile gives me anxiety. Ahhh!" she screams. "I'd try to be fair in answering my questions, but you think, 'Who's the freak I'm going to meet?' and 'How do I know if any of this is true?' I'd be terrible at it!"

Fortunately for Johansson, 29, she's already found Mr. Right. Last summer she got engaged to Romain Dauriac, 31, a French journalist who manages a creative agency. "Being engaged is an exciting time to enjoy with a guy I'm deeply in love with," says the actress, snuggling up on a couch with a blanket and some candy at Manhattan's Gramercy Park Hotel. As for wedding plans, they don't want to "rush through it," she says. "It's very romantic."

An actress since age 9, Johansson is also hitting a new stride in her career. She earned acclaim for the Oscar-nominated Her as well as the racy indie comedy Don Jon and Cat on a Hot Tin Roof on Broadway. Up next she has a sci-fi thriller, Under the Skin, a return as slinky superhero Black Widow in the next Captain America movie and even a Super Bowl commercial for SodaStream (she's an avid cook). "She's in some Renaissance age where she is pushing herself to new places," says Her director Spike Jonze. "She wants to go deeper and is taking risks." But she didn't see playing sensitive computer Samantha as that much of a stretch. "I can relate to her enthusiasm, her curiosity and her tenderness - those are all feelings that come from my heart too," she says.

There's also lots of joy offscreen. After her two-year marriage to Ryan Reynolds ended in divorce in 2010, Johansson dated Sean Penn and ad executive Nate Naylor. In 2012 she met Dauriac through friends, and he popped the question last August. A native New Yorker, Johansson moved in with him in Paris, where they've been spotted checking out the art and indie music scenes. "The most important thing I've realized through my experience in past relationships is that I really want to be friends with my partner more than anything," she says. "Of course it's important to have passion, but you can't always be in the honeymoon phase. The friendship is really what carries you through when you have ups and downs. And to have somebody who believes in you and can tell you if you're being irrational or make you feel assured when you're feeling doubtful."

She has that in Dauriac. "He's someone I can always rely on," she says. "He's my buddy. I'm very happy!"