FORTUNE — Larry page loves moon shots, so it’s fitting that as CEO of Google (GOOG) he has entrusted the company’s most ambitious endeavors — self-driving cars, for example — to his closest friend, confidant, and collaborator, Sergey Brin.
Even before they became known as the Google Guys, their fellow graduate students at Stanford called them “LarryandSergey.” After they achieved worldwide fame by creating the sophisticated algorithms that powered their search juggernaut, they still worked in unison from a shared office in the Googleplex. By any measure, theirs is one of the most successful partnerships in business history.
Two years ago Page, 39, stepped into the spotlight to become CEO, while Brin, also 39, receded into the background. Their partnership, rather than dissolving, has morphed, but by all accounts continues to bear fruit.
Brin now runs special projects, including Google X, the company’s skunkworks. In addition to self-driving cars, Brin’s group has come up with Glass, Internet-connected, augmented-reality eyeglasses that should be available to developers this year. Brin, who often wanders the Googleplex in shorts and Five Finger shoes, wears the glasses all the time. He loves to work on completely new things, he says, and the more tempered pace of Google X suits him — he is famously allergic to scheduling. “My big regret,” Brin says, “is that I didn’t make this change years ago.”
Page keeps Brin close. “He knows the company inside out,” Page says. On Mondays, Brin attends Page’s staff meetings with Google’s top brass. Last fall, when a problem with Page’s vocal cords kept him from speaking, Brin ran the meetings. “He spends a lot of time with my team,” Page adds.
At Google X, Brin has brought focus to some of Page’s priorities — making Google’s products more beautiful, for instance. Such concentration may have paid off: At Fashion Week in New York last year, several models showcased Diane von Furstenberg’s new collection while wearing Google Glass.
Times change, but Page and Brin still are the Google Guys, in pursuit of a more connected tomorrow. “X really embodies Google’s spirit, which is to take technology and turn it into something transformational for the world,” Brin says. Busy with the nitty-gritty of running a giant corporation, his friend, and now boss, says he wants Google to scale its ambition. In other words: Page and Brin want more moon shots.
–Our Face to Face series examines successful business partnerships that offer lessons on collaboration and compromise.
This story is from the February 25, 2013 issue of Fortune.