It's fair to say that no audience in history has ever seen anything quite like him. And for opera, that's just the problem -- after Domingo, then what? Correspondent Scott Pelley reports.
"I always said if I will be able to sing the way I know it should be done, I will be the greatest singer in the world. Because I know exactly what I have to do it. Except then I cannot do it," says Domingo, who says he's never been completely satisfied with his performance on stage.
"That's the problem. At any time in my life, I don't think I have been able to sing exactly the way it crosses my mind and it should be."
Now, at the age of 63, Domingo is searching for the next generation of opera stars. Who's he betting on? Well, there's a woman who was selling cleaning products door-to-door and a former football player from Florida.
How's he finding them? We followed Domingo on the talent hunt to Paris. He's rehearsing young singers he's discovered through his annual competition. It's a worldwide talent search he calls Operalia -- sort of his own version of "American Idol."
Every year, approximately 1,000 singers from all over the world apply to Operalia. Judges choose 40 to come to the competition. It doesn't matter if they can't afford it -- all expenses are paid. In the end, 10 singers are finalists who perform in concert.
In Florida, John Matz was a high school football star who used to sing the national anthem before his own games. Matz studied singing in college, and in Operalia, he was the top tenor. Here, he's suited up for a dress rehearsal.
"I just have such great respect for him. I mean, he's a hero, somebody that I've always watched, always listened to and never really thought that I would ever be that close to at any time," says Matz. "It's because of him and the belief in the young artist, and giving the opportunity to say, you know, 'I believe in them. They can do it. Give 'em a chance.'"
Later that night, Paris gave Domingo's protégés a chance. By the end, stars were born in the city of light. Some were thrilled; others looked like it was the most traumatic experience of their lives. Domingo taught the first rule of the encore -- go out only if they demand it.
The morning after, on the Seine, Pelley asked Domingo about something he saw on stage that surprised him: "You were pushing all these young people out ahead of you onto the stage. I think a lot of people would say that's not what a star does. A star leads out onto the stage."
"I see them just like my children, and I am here, you know, just to try and help you. That's the way, you know," says Domingo. "You cannot be so vain than, than is OK, so here I am. You know, and here they are coming behind. I think it's wonderful that they are coming forward."
"I think for me, one of the great passions and great love that I have in music is the continuation -- always in the old times, the singers used to say 'No, after us, nobody's there,' and I completely, is completely wrong attitude," adds Domingo. "I think no, only than people they are coming out every day. But that you have to prepare them to be exactly that generation of singers and they will excite the whole musical world."
What happens to a singer after Domingo pushes them on stage? Pelley talked to Veronica Villaroel, who was selling cleaning products door to door in her native Chile before she discovered her voice.
After Domingo heard her, she started performing in the biggest houses around the world. "He gave me the opportunity to make my career bigger," says Villaroel.
Now, she's playing opposite Domingo in a production of "Pagliacci," where the insanely jealous clown ends his marriage in a traditionally operatic way.
"The way he looks at me, those eyes. And that energy he had, and everything was right there. And he's, you could see his energy blowing, you know? And I was really scared for my life," says Villaroel. "And I love that. Makes me feel! I think everybody wants to feel!"
The feeling you get with Domingo is that he may be the hardest working man in show business. He's the artistic director for both the Washington National Opera and the Los Angeles Opera.
This season, he'll spend 27 nights conducting, sing eight solo concerts and play the lead in 47 opera performances. He's fond of saying, "If I rest, I rust."
So why has opera's biggest star become its busiest talent scout? It may be because of the way he was discovered. As a teenager in Mexico City, his mother, an opera singer, noticed his voice.
"I hit a note and when I hit that note I see the tears coming out from the eyes of my mother," recalls Domingo. "And I said, 'What happened to you? And she said, 'Your voice. That's a real voice. That's a real voice.'"
60 Minutes caught Domingo in Wagner's "Die Valkurie," playing Sigmund, a brutal job for tenors half his age. After the opening act, he ran off stage and tutored the makeup artist in the art of a proper scar. And while others were on stage, we found him in what looked like a coat closet, working on the next act – still unsatisfied with how he was doing.
If Domingo's never been satisfied with his own voice, we wondered whom he did admire. It turns out, it was more Vegas than Wagner.
"I have a great admiration for what Sinatra was doing. I think Sinatra, the way that he sings, the phrasing, a certain resonance that continues a little bit the voice when you stop it," says Domingo. "It is when you stop singing it's kind of in the air, the voice is still there. I like it very much."
What does he think of today's popular music?
"In the popular music, there are beautiful melodies still that you heard. And that there are other things that I don't understand anything," says Domingo. "It's the same thing, and the same thing and the same thing. But perhaps, it's easy for people to follow that. I understand. I respect everything that is successful."
For instance, rap. He says he doesn't understand it, but he has to respect it: "It's not my fault if I don't understand, you know. But I respect it. I think it should be like they say it, cool."
While he's preparing the next generation, Domingo is not bowing out. He is fully booked in major operas for the next three years. At that time, he'll be 66.
Will he know when it's time to stop singing? "I have to know it. I have to know it. There are two ways of doing it," says Domingo.
"You plan and you said, 'Ok, so that's it. This year is going to be my last year, and I sing two performances in every theater. Or, one day, you just go out in front of the public and say, 'Ladies and gentlemen, tonight has been my last performance.'"
"I don't believe in saying just like in some of the operas goodbye, goodbye, goodbye, goodbye, goodbye," adds Domingo. "No, no. Once you say it, goodbye, it should be goodbye."
When will that be? Well consider this. The New York Times once ran a review that said Domingo was at his peak and it couldn't last much longer. That was 23 years ago.