Leonard Cohen the artist has long been hailed as a musical giant, but the man has been something of a mystery. The Jewish singer/ songwriter’s most famous composition, “Hallelujah,” started out as a sacred song about King David but became a pop music perennial, covered by a dizzying array of singers. Both the singer and the song are the subject of the excellent documentary “Hallelujah: Leonard Cohen, a Journey, a Song.”

The film is billed as a “definitive exploration” of Cohen’s life and career, and indeed it is, offering insights into the man, his deep connection to his Jewish faith and his process as a writer. The film also is a kind of double biopic on the life of the songwriter and the story of his most famous song, both of which had a rocky journey to fame.

Co-directors Daniel Geller and Dayna Goldfine structure the documentary as three acts, beginning with a more familiar biopic of Cohen’s early life and career, switching to a “biography” of the song (how it was written, its many versions and its slow, unexpected rise to fame), and then returning to Cohen’s journey, including how the unexpected success of the song affected his later life.

Using archival stills, extensive interview footage of Cohen, live performances and interviews with those who knew him, this documentary dives deep into Cohen’s life and work as a poet and a songwriter. The path of his career is balanced with his explorations of his Jewish identity and faith, his interest in Kabbalah, his long sojourn into Zen Buddhism, and then his return to Judaism.

Interview subjects range from musicians such as Judy Collins, Rufus Wainwright and Glen Hansard to important figures in Cohen’s life, such as Rabbi Mordecai Finley, who led the synagogue Cohen attended in his final decade.

Cohen was born in Canada to a wealthy Orthodox Jewish family in Quebec. His Lithuanian-born mother was the daughter of a rabbi and Talmudic scholar, and prominent figures in Jewish life were on his father’s side as well.

Cohen came to music a bit late, at age 30, when he was already a novelist and a poet acclaimed in literary circles. His writing and later his song lyrics were honest and open rather than comforting, with a knowing, dark humor.

When he turned to music in the late ’60s, he was embraced by Collins, Bob Dylan and other folk-rock greats, and he developed a cult following. Wider fame eluded him, however, even as other musicians loved his songs and their poetic, deeply thoughtful lyrics that didn’t always fit into neat categories.

Collins, who scored a hit with her version of Cohen’s “Suzanne,” speaks in the film about the deep influence of Cohen’s Jewish upbringing on his work.

Cohen is asked whether he had considered changing his name, as Bob Dylan and others had done by dropping more Jewish-sounding surnames. Cohen slyly replies, deadpan but with a glint in his eye, that, yes, he considered changing his first name to something more Jewish, as his last name was already Jewish enough, cleverly undercutting the question and displaying his quick wit.

The eventual success of “Hallelujah,” which was released in 1984 on Cohen’s album “Various Positions,” gave Cohen a late-in-life career boost until his death at age 82 in 2016.

What about that song? Cohen worked on “Hallelujah” for more than seven years, and it is thought to have had as many as 180 draft verses. Around the time he was writing the song, Cohen had been exploring Kabbalah and Jewish belief. The song started as something sacred, about King David composing a song, set to a 6/8 time signature evoking waltz and gospel music. Cohen recorded a sacred version on “Various Positions,” which his label, Columbia Records, disliked and declined to release in the United States (although an independent label did release it).

As Cohen toured, the lyrics evolved from sacred to secular, with some verses frankly sexual. Meanwhile, other musicians took note of the song. John Cale recorded a cover of it in 1991, combining verses from the sacred and secular versions, which was followed by Jeff Buckley’s recording of that version in 1994. A music producer working on the animated movie “Shrek” (2001) took the Buckley version, sanitized the lyrics, and included it in the soundtrack. A phenomenon was born.

The documentary follows the song’s long and winding road, which takes some very surprising turns, and we hear Cohen reflect with a kind of paternal pride on the impact the song had on his later life.

One intriguing aspect of the film are excerpts from Cohen’s songwriting journals, giving a rare glimpse into his process. Interviews also support this focus, delving deep into Cohen as a poet/songwriter and Jewish spiritual explorer. A long period of living at Zen monastery is followed by a return to Judaism and life as a musician.

Unlike another recent film about Cohen, “Marianne & Leonard: Words of Love,” this documentary focuses more on Cohen’s artistic life than his love life, although it does note Cohen’s reputation as a “ladies’ man.” Interview footage with French photographer Dominique Issermann, who was in a long relationship with Cohen while he was writing “Hallelujah,” has her talking more about the song and songwriting than the affair.

There is so much that is surprising, intriguing, and deeply insightful about Cohen’s life in this film, and co-directors Geller and Goldfine do a marvelous job of bringing all that out and weaving it all into a very enjoyable and informative experience.