He has been full of surprises. "Company," which opened on Broadway in 1970, was the first musical without a defined, linear plot. "Sweeney Todd" debuted on Broadway in 1979 and featured the "Demon Barber of Fleet Street," while, on a sweeter note, the 1987 Broadway production of "Into the Woods" was a delightful romp through children's fairy tales about what really happens after "happily ever after."
Despite his massive success, Sondheim also has been met with fierce critics over the decades, many of whom have said his music is too cold, impersonal, difficult to sing and lacks mass appeal. Sondheim doesn't seem fazed by them.
"I think it's the only one of the arts that's mostly reviewed by ignoramuses, people who know nothing about what they're writing about," he said, although he admitted that when "Sweeney Todd" first opened, it lost two-thirds of its money.
Whatever small struggles he has encountered in the past, there also have been stunning successes. "A Little Night Music," now in revival on Broadway, features one of the most iconic songs ever to hit the stage and perhaps the most famous song Sondheim ever wrote: "Send in the Clowns."
Peters, who recently took over the role of Desiree from Catherine Zeta-Jones in the revival, is the most recent actress to sing the powerful song.
"What's funny about Steve's songs is you think, 'Oh, this is about something,' and then you start working on it and you go, 'No, it's about something,'" Peters said. "It goes even deeper than you imagined."
As for "West Side Story," despite Sondheim's grumblings, the musical was produced by a Broadway all-star team, with music by Leonard Bernstein, direction by Jerome Robbins, and Sondheim's lyrics, which he penned in his early 20s.
"Most of the lyrics were sort of ... they were very self-conscious," he said. "Bernstein wanted the songs to be ... heavy, what he called 'poetic,' and my idea of poetry and his idea of poetry are polar opposites. I don't mean that they are terrible, I just mean they're so self-conscious."
There is one bad song in particular that stands out for Sondheim, one that Jack Nicholson turned into a hilarious parody in the film, "Anger Management," as many others have done.
"I'm fond of quoting 'I Feel Pretty,'" Sondheim said. "The street girl is singing, 'It's alarming how charming I feel.' ... I just put my head under my wing and pretend I'm not there."
Although all of the composer's great work has continued to live on and be celebrated, he said being immortalized isn't important to him.
"I'm one of those people why doesn't care about posterity," he said. "There are people who care; I couldn't care less what happens to my stuff after I die because I won't be around to enjoy it."
ABC News' Lauren Effron contributed to this report.