In the past two years, she has had six number-one hit songs, and on Sunday at the Grammy's she is not only a headline performer, she has also been nominated for six awards.
Her fans are devoted to her, and millions more seem mystified by her. Is she a real artist or a marketing expert? Is she musically gifted or a flash in the pan?
We weren't sure what to expect when we caught up with her in the final months of her sold-out European tour.
Her real name is Stefani Germanotta and she's just 24 years old.
Each time we met her she surprised us - not just with her candor, and her frank talk about drugs may concern some parents, but she also surprised us by never appearing the same way twice.
Veteran producer John Hamlin followed Lady Gaga from London to Milan to New York. Hear the stories from the road, get a tour of Gaga's dressing room, and see the pop star's emotional moment we saved from the cutting room floor.
What did Lady Gaga, Madonna, and Barbra Streisand all do behind the scenes on their "60 Minutes" shoots?
CNN's Anderson Cooper sits down with "60 Minutes Overtime" editor Ann Silvio to share more revealing moments from his series of in-depth interviews with Lady Gaga.
Segment: Lady Gaga
Extra: Lady Gaga Explains The Meat Dress
Extra: Lady Gaga And Her Fans
Extra: A Martyr For Show Business?
So how does one address her?
"Call me Gaga," she told CNN's Anderson Cooper.
When asked if anyone calls her Stefani, Lady Gaga said, "Yeah, some people do. Especially in bed…I prefer Stefani in bed."
"Really?" Cooper asked. "You don't want somebody yelling out, 'Lady Gaga'?"
"No. That would freak me out," she replied.
When we first met Lady Gaga in London, we had planned a quiet stroll along the River Thames. But when she arrived, about a dozen paparazzi were following her.
When Cooper asked if she ever gets used to the paparazzi, she said, "No."
Make no mistake: Lady Gaga uses the photographers as much as they use her. Her over-the-top outfits are designed to grab headlines and get people talking.
"Everywhere you go, are you always in full regalia?" Cooper asked.
"Full regalia. That's a fabulous word! Can I steal that from you?" she replied, as she walked in 10-11 inch platform shoes.
To get away from the paparazzi, she took us to the outskirts of London to a small pub for a drink.
"Do you take days off? Or do you feel like you're in this whirlwind and you have to keep it going?" Cooper asked.
"Right now, we're in a bar, right? And there's a camera right there and a camera right there," she said, pointing around the room. "But if I were to be sitting in this bar, and we didn't have a scheduled interview, there would still be a camera over there and over there and over there. I'm always on camera."
"From what I understand, you are a student of music. You're a student of fashion. But you're a student of fame, in a way," Cooper remarked.
"One of my greatest artworks is the art of fame. I'm a master of the art of fame," she replied.
To understand how Lady Gaga got so famous, you have to start with her music.
She's been on tour for much of the past three years. A tireless performer, in concert she is constantly on the move, singing, dancing and changing costumes.
Her biggest hits are dance songs and some of the imagery may seem reminiscent of Madonna. But Lady Gaga is more outrageous.
She has studied the artistry of others but is a creation all her own, a classically trained pianist who writes or co-writes all her songs.
She insists she never lip synchs, and alone onstage, her voice packs a powerful punch.