The question most inevitably asked of songwriters is always, "What comes first, the words or the music?" Lyricist Sammy Cahn, whose centennial is being celebrated this year alongside that of his most celebrated partner, composer Jimmy Van Heusen, had a ready-made answer: "The phone call." It was his favorite quip—he said it not only to me, he repeated it on every interview or public appearance, and with good reason. Cahn and Van Heusen wanted you to think of them as professionals first and artists second; to hear them tell it, they didn't write music to express anything like an aesthetic longing in their souls, but rather they were something akin to musical tailors, crafting product for the specific needs of artists, producers and the marketplace.

Sammy Cahn and Jimmy Van Heusen wrote such hits as 'All the Way,' 'Love and Marriage' and 'Ev'rybody Has the Right to Be Wrong.' Getty Images

Yet any listen to the hundreds of songs that they wrote together, from 1955 to 1972, shows that they were poets of the highest order: Their songs combined Van Heusen's sweeping melodies—musically ingenious and harmonically profound—with Cahn's incisive lyrics, at once warm, witty and heartfelt. They could be wryly cynical in poking fun at the social conventions of the day ("Love and Marriage") or heartbreakingly sentimental ("Incurably Romantic"). Even when writing a rhythmic bauble like "Ring-a-Ding-Ding" or "Come Dance With Me" for their No. 1 client (and best friend), Frank Sinatra, the construction and craftsmanship on their work was remarkable, and it was perhaps even more so on their slow-tempo love ballads, like "Only the Lonely" or "I'll Only Miss Her When I Think of Her."

As singer and scholar Michael Feinstein —who began his most recent show in New York with the team's "Fancy Meeting You Here"—puts it: "Cahn and Van Heusen were a dynamic combination, being so modern in what they brought to songs of their era: jazz, snap, swagger, heart and great craft. They could write any kind of song, from the theatrical faux-1920s 'Thoroughly Modern Millie' to the lyrically dazzling 'Ev'rybody Has the Right to Be Wrong' to the yearning 'All the Way' to style-defining songs like 'Come Fly With Me.'"

The majority of the team's most famous songs were written for Sinatra—as themes for his movies or title numbers for his concept albums—but in 2013, it seems like the whole world is singing their songs. Steve Tyrell themed both his forthcoming album and his most recent show at the Cafe Carlyle to the lyrics of Sammy Cahn. Mr. Feinstein is devoting his February concert at Zankel Hall to the team. The Turner Classic Movies channel will feature two nights of their movies, on Jan. 24 and 25, followed by the premiere later this year of a new documentary, "Swingin' on a Star—the Music of Jimmy Van Heusen" by James Burns (and featuring this writer among many talking heads). Perhaps most impressively, their film score to the 1964 movie-musical "Robin and the 7 Hoods" is being adapted into a full-scale Broadway musical for the fall.

Although originally from New York (Van Heusen was born Chester Babcock on Jan. 26, 1913 in Syracuse; Cahn was born June 18 that same year in Manhattan), Cahn and Van Heusen were the top songwriters in Hollywood during the final years of the old-time studio system; they wrote relatively few traditional musicals but were the masters of the movie main title theme for a drama or comedy. Between the two of them, they earned five Oscars for Best Song: one each individually, then three as a team: "High Hopes," "All the Way" and "Call Me Irresponsible." (Cahn insisted to me that "Love and Marriage," which won an Emmy, should also be counted on that list, since it was an award presented by an academy.) Like Rodgers and Hammerstein, they were a second marriage. Both had enjoyed considerable success in the 1940s with other partners, Van Heusen with Johnny Burke (writing, among other things, nearly all the songs for Bing Crosby's pictures), and Cahn with Jule Styne (who, similarly, wrote most of Sinatra's early movie-musicals), but did their best remembered work together.

It was Sinatra himself who brought the two together in 1955, to write the songs for his film "The Tender Trap" and then "Our Town," a unique television-musical adaptation of the Thornton Wilder play (which yielded "Love and Marriage" and the beautiful "Look to Your Heart," among others). They each were longstanding friends of the Chairman, who gravitated toward different aspects of their personalities. "Sinatra spends his days with me and his nights with Van Heusen," Cahn famously said. "Jimmy was a bachelor, Sammy was married and raising two children," as Sammy's widow, Tita Cahn, points out. "So their lives were very different, but they were good friends and they had a very healthy and productive collaboration for a long, long time."

In the Burns documentary, Frank Sinatra Jr. says, "Van Heusen understood Sinatra's style of singing; Sinatra understood Van Heusen's concept of melody." Mr. Feinstein elaborated, "Sinatra always stayed true to what they wrote because they imbued those songs with his persona and he didn't have to change anything or interpolate hip phrases to make them his own. It was the perfect combination of writer and singer."

Van Heusen supplied the singer with more than repertoire—his lifestyle was a virtual template for the Sinatra persona. The high-rolling, footloose and fancy free bachelor that Sinatra plays in "The Tender Trap," "Come Blow Your Horn" and many of his other comedies of the period was closely modeled on the composer, who was a well-known ladies man. "The trouble with Sinatra," as Cahn said in another of his famous quips, "is that he thinks he's Van Heusen."

And yet Hollywood's ultimate swinging bachelor, who didn't marry until comparatively late in life at 56, composed some of the most moving songs ever about long-term commitment, such as "All the Way," "To Love and Be Loved" and "All My Tomorrows." As Woody Allen says in Mr. Burns's film, "For the same reason that Gershwin or Cole Porter or Irving Berlin endure, he was just a gifted songwriter, and he's got a large number of songs that are just as fresh. They're not clichéd, they're not corny, they represent a certain sort of a romantic feeling." Early on, Van Heusen was the more outgoing of the two, as a prominent member of the New York and then Hollywood night-life scene. (The composer, whom Cahn described as a hypochondriac, was nevertheless not afraid to risk his life to serve as a test pilot during World War II.) In the final part of their lives, they did a turnaround. Van Heusen went from man-about-town to recluse, and Cahn became more prominent, touring with a one-man show where he sang his own songs and talked about his career.

Cahn made it to age 79; Van Heusen to 77. When I interviewed Cahn in 1991, after a few hours of talking about his old songs, he interjected: "You don't go back. You go onward. Jimmy Van Heusen and I have a philosophy: You write the best song you know how to write."

Mr. Friedwald writes about jazz for the Journal.