A documentary by Asif Kapadia. Rated PG.

Why should we still care about Amy Winehouse? Well, it turns out this tragic young Englishwoman made an indelible mark on music. By tapping into the tones and attitudes of jazz and soul divas past and fusing them with a highly original compositional style, she inspired a wave of singer-songwriters, including Adele, Lianne La Havas, and Lady Gaga. And she was just hitting her stride when she joined the 27 Club, in 2011.

At 128 minutes, the feature documentary Amy could have included a couple of complete songs. But U.K. director Asif Kapadia makes the case for her greatness, and her downfall, almost entirely through her own actions.

As in his compelling Senna, which laid out the dark trajectory of the Brazilian race-car driver, he uses other voices, mostly off-screen, to move the tale along. But the focus stays on this feisty North Londoner, skipping school to write songs in the late ’90s, and documenting everything with her mates.

That’s something that separates this engrossing saga from portraits of now-historical figures: everything is so recent! So we get good-quality home movies, plus raw footage of events like her record-company audition, in which she sings flawlessly, accompanying herself on acoustic guitar—badly, but with the complex chords of an academy graduate. (The sound is phenomenal throughout.)

Winehouse knew what she was doing, from songcraft—her diaristic lyrics appear on-screen—to image-building, even if she soon became trapped by the latter. Like Billie Holiday, she wasn’t able to separate musical suffering from real life, and she shared Lady Day’s taste in men, seeking out unworthy swains whose main skills involved exploitation and sloth.

The movie hints at the violence she also dished out on her pathetic husband, Blake Fielder-Civil, and much of her self-destruction could be called an extended cry for help aimed at her slug of a father, who ignored teenage bulimia and an intense need for, as the song says, rehab. In the end, though, this is about music.

As Tony Bennett says, in one of the most touching sequences, “She was a jazz singer, and jazz singers don’t want to sing for 50,000 people.”