Of the rich commentaries in “Fiddler: A Miracle of Miracles,” the observations of Broadway legend Stephen Sondheim are among the most meaningful.

As a young composer, actively working in the theater at the same time, Sondheim’s mixture of praise and envy add texture to this rich documentary. And his comments remind anyone who loves Broadway of the magic this composer has created. While primarily known as a composer and lyricist for the Broadway stage, his work has enhanced movies for almost 60 years.

Of course, Sondheim’s first musical, “West Side Story,” was so beautifully filmed in 1961 by Robert Wise that it won the Oscar for Best Picture. Even though Sondheim contributes some of his most touching lyrics, this musical belongs more to the driving melodies of Leonard Bernstein and the remarkable dances of Jerome Robbins. More than 55 years later, the film still amazes with the energy in its movement and the depth of its emotional content.

One year later, Sondheim experienced with “Gypsy” what can happen to a show when the Hollywood experts cast the wrong star. On stage, his lyrics — to the music of Jule Styne — detail the turbulent backstage life of Gypsy Rose Lee in a show that many consider the Broadway’s best. While the role of Mama Rose has been played on Broadway by such names as Ethel Merman (the first), Angela Lansbury, Tyne Daly, Bernadette Peters and Patti Lupone, the screen assignment went to Rosalind Russell. And while she is touching in some later scenes, Russell never establishes the character’s drive to make stars of her children. That makes it difficult to sympathize when her fortunes change.

While Sondheim experienced his first success on Broadway as a composer and lyricist with “A Funny Thing Happened on the Way to the Forum” in 1962, it suffered its way to the screen in 1966 when director Richard Lester decided to cut a lot of music to focus on the story’s comic elements. What he overlooked, though, is that a musical is all about music, and a musical without the necessary music doesn’t always make sense. Despite a funny performance from the reliable Zero Mostel, and strong support from Phil Silvers, those who wandered into Forum in a movie theater may have wondered what all the fuss was about.

Musically, “A Little Night Music” features one of Sondheim’s most ambitious scores with the songs written in 3/4 time to create a collection of lovely waltz melodies. The composer brings those melodies to life with some of his most insightful lyrics as he examines the follies of human relationships. While this show can be an intensely theatrical experience, it begs for a visual treatment, especially when the narrative shifts to the country in the second act. But there’s nothing visual in this stage-bound adaptation directed by Harold Prince who also directed the original on Broadway. While Hermione Gingold and Lou Cariou effectively recreate their stage roles, and Diana Rigg makes a saucy appearance, the casting of Elizabeth Taylor in the role created by Glynis Johns is a bit of stunt casting that backfires. Taylor looks bored with the dialogue, uncomfortable in the costumes, and intimidated by the score. Her rendition of the magical “Send in the Clowns” is painful.

Leave it to Tim Burton — perhaps a surprising choice to direct a Sondheim musical — to create a most effective screen adaptation of “Sweeney Todd,” the tune-filled exploration of a man who seeks revenge in unusual ways. With Johnny Depp revealing surprising musical sense, and Helena Bonham Carter using her little voice in a big way, Burton creates a world that would make Sondheim proud. While the score had to be cut to fit the running time, the magic of the work shines through. We get from the movie what Sondheim originally intended.

Like Burton, Rob Marshall demonstrates a real respect for Sondheim, and an appreciation for what makes his work so special, in the film version of the fairy tale musical, “Into the Woods.” On its inspired journey from stage to screen, this musical retains all of its magic from the stage as it transforms into a rich visual experience. Rather than recreate the theatricality of the original, director Marshall reimagines the material. The result is a musical dream from start to finish. For Sondheim, the man who reinvented the Broadway musical, “Into the Woods” preserves the essence of a work that reveals so much of his heart. With lovely melodies — and lyrics that shine with humor and understanding — he makes us wish we actually could live in those woods. If only we could sing.