Vitali, who's 6 feet, 8 inches and weighs 250 pounds, just won the World Heavyweight Championship. His little brother, Wladimir, is slightly smaller, at 6 feet, 6 inches and 245 pounds.
Correspondent Dan Rather met with the Klitschko brothers a month ago in Los Angeles, as they were both training for upcoming fights.
Everyone agrees that the brothers are both very good boxers. Their size alone gives them incredible reach, and they work very hard at their craft – and take the science of boxing very seriously.
The brothers grew up in Kiev, the capital of Ukraine. Their father was a colonel in the Soviet Air Force, and they were the children of the Cold War.
"Our father believes in this system," says Vitali. "It was a party, Communistic party," adds Wladimir. "And God was Stalin or Lenin."
Vitali, who is five years older than Wladimir, started boxing in his early teens and quickly developed a work ethic that stays with him today.
At 18, he traveled to the United States for an amateur fight, and says it was a real eye-opener for a child of the Soviet Union: "All my life, I heard about this country, just bad things. I can't believe, why are the people so friendly? Why is it so nice here and why is life so strange and difficult in the Soviet Union?"
Vitali brought some souvenirs back from his trip, including the ultimate symbol of capitalism - a bottle of Coca-Cola - for his younger brother.
"So, I open this, the top of Coca-Cola very slowly, and the first thing, I just smell it. It was very sharp," recalls Wladimir, laughing. "But it smells America. It was very interesting for me. ... This is how the American freedom smells like, you know?"
The younger Wladimir soon followed his brother into the ring, and quickly became a top amateur. He won the gold medal as a super heavyweight in the 1996 Olympics, but it was always his older brother, Vitali, who led the way.
Although they had other options, the brothers decided that boxing offered the best opportunity for fame and fortune. It was, they felt, an ancient and honorable sport.
"The rules in boxing doesn't change for a very long time, for thousands of years, still the same, actually," says Wladimir. "It's just two gentlemen who talk to each other with the hands, and try to explain who is more right, you know?"
But the brothers soon realized that if they really want to succeed at boxing, they have to do it in the United States. They moved to Los Angeles and began the long run toward the top of the boxing world. Vitali has won 32 fights – all but one with knockouts – and lost only two. Wladimir has 42 wins.
Inside the gym, the hard work goes on under the watchful eye of legendary boxing trainer Emmanuel Steward, who has trained many heavyweight champs.
"[They] could become all-time greats," says Steward. "Wladimir is more coordinated, but the older brother, Vitali, is more intense, actually has more of a mean streak in him."
However, the Klitshko brothers are more than just boxers. They both earned Ph.D.s from Kiev University in sports science, and they like literature, politics and art-house films. But they also share another intellectual pursuit that 60 Minutes II learned about when we met Vitali at a South Los Angeles marina, near the apartment the brothers share while training.
Vitali is very good at chess, and he once lasted 31 moves against world champion Garry Kasparov. When Rather challenged him to a game, his trainers urged him to throw in the towel after only 10 moves. "You win, I concede," says Rather.
But how can a man with so many interests give boxing the focus necessary to become the best? "We tried to develop, try to enjoy the life from many, many sides," says Vitali.
Vitali and his wife, Natalie, and their two young children now live the Los Angeles lifestyle. Wladimir is still single.
Both brothers visit their parents in Kiev often, but their parents never go to their fights. Vitali made that rule early in his career, after his opponent once brought his family to the fight.
"It happened, I knock him out, and I see the eyes of his mother, father, wife," recalls Vitali. "And after that, I tell my parents, my family, never will you be in the fight. It's too big pressure for me, emotional pressure."
Now, the Klitschkos are also under pressure from a boxing world desperate for new stars. And the giants from behind the Iron Curtain have become the great red hopes of boxing.
60 Minutes II wanted to know why the boxing establishment has such a big investment in the Klitschko brothers. So we met boxing commentator Max Kellerman at a popular boxing hangout near New York's Times Square, for an assessment.
"Neither one is perfect, neither one jumps out at me as being dominant, great fighters, but they're both good," says Kellerman. "And they're both really big. And it would be a tall order for anyone to beat either guy."
One reason boxing has become a marginal sport, says Kellerman, is because there are no Joe Louises, Rocky Marcianos or Muhammad Alis in the ring. And without that kind of star power, boxing has become a series of bouts between anonymous fighters on late-night cable TV.
But is boxing really a sport for the masses?
"Boxing is, in fact, everybody's favorite sport," says Kellerman. "If you come to an intersection and on four corners you see the following. On one corner, there's a couple kids playing stickball. On the other corner, there's some guys that are shooting hoops. On a third corner, there's a guy just standing there putting a golf ball. And on the fourth corner, there's a fistfight. There are a hundred people at the intersection. How many people are watching anything but the fistfight?"
Kellerman believes boxing's draw is its combination of power and fear. Rather asked the Klitschkos how they deal with those primary elements during a fight. Are they afraid?
"If you don't have fear anymore, you are a loser," says Wladimir. "The fear is a gift from God. And you have to know how to use it. It motivates unbelievably. And it makes you faster, smarter, better."
Faster and better is what everyone expected Wladimir to be two weeks ago when he met Lamon Brewster in a fight in Las Vegas. As always, Vitali was in his corner, watching Wladimir dominate Brewster, landing punch after punch.
But by the fourth round, Wladimir seemed to run out of gas, and Vitali looked on in anguish. And in the fifth, Brewster landed two good punches, and Wladimir just couldn't make it back to his corner. The referee ended up awarding the fight to Brewster.
That was Wladimir's second stunning loss in a year. He was humiliated last March, when South African heavyweight Corrie Sanders surprised him with a knockout punch in the second round.
In the ring, right after that fight, Vitali seemed determined to beat the guy who had beaten his kid brother. And he had his chance on April 24, thanks to a dominating win over Sanders for the World Heavyweight title.
With Wladimir's boxing future now in doubt, it falls to Vitali to redeem the family honor.
Will Vitali's win change Kellerman's mind about his potential to be a dominant heavyweight champion?
"That's the drama. That's why the story is worth listening to. Because you don't know what's gonna happen," says Kellerman.
But there's one thing the Klitschko brothers insist will never happen: fighting each other.
"We don't want to see our mother crying. And we don't want to break our mother's heart. And we promised our mother when we start to box, we will never fight against each other," says Wladimir.
Even for big money?
"Money is very important point in life," says Vitali. "It's not everything." Adds Wladimir: "It will never happen."