By many measures, Joan Jett is one of the most influential figures in rock history. But how many young fans who adore her proto-punk attitude would guess that one of the rocker’s early influences was … Liza Minnelli?

“I wanted to be an actor before I fell in love with music,” Jett, 59, explains in an interview with Variety. “And ‘Cabaret’ was really the combining of the two. Seeing that, with its ’20s flapper girl decadence and the crazy makeup, around the same time I started wanting to play guitar, it all sort of melded together into this sort of slightly decadent-looking vibe — I mean, I didn’t quite have that at 13, but it was developing.”

Her career path veered decidedly to music, but she hasn’t been a stranger to the screen. The camera loved her from the moment she stepped out in red leather in 1981 for “I Love Rock ’n Roll,” one of the first true MTV-bred hits. Six years later, she took the lead opposite Michael J. Fox in Paul Schrader’s “Light of Day,” and she’s occasionally turned up since in places as unexpected as “Walker, Texas Ranger.” Her pioneering 1970s ways were immortalized for a new generation with Kristen Stewart’s portrayal in 2010’s “The Runaways,” which Jett executive produced.

Now she’s playing herself in “Bad Reputation,” a documentary that premieres at Sundance on Jan. 22, preceded by a live gig at the Park City film festival Jan. 20.

It was preordained that the film would be named after her 1980s signature song and album, but the title is a bit of a misnomer: If there’s any rocker who doesn’t require much image rehabilitation at this point, it’s the nearly universally loved Jett. “Bad Reputation” is really part of a victory lap, coming on the heels of not just that biopic about her seminal all-girl band but her 2015 induction into the Rock & Roll Hall of Fame. That’s not to say the new doc feels unnecessary: As producer Carianne Brinkman says, “It’s wonderful that the Runaways’ story was told, but I didn’t think we were done telling a story about Joan Jett. I think it’s a really important story, especially for young girls to see, and also young boys.” The goal may be a tip-off that the movie’s story is less about decadence than, in Jett’s mind, “perseverance.”

Brinkman is the daughter of Kenny Laguna, a writer-producer-manager whose run of 1960s hits has long since been eclipsed by his nearly four-decade partnership with Jett. Beyond playing up the historicity of one of the first and foremost female rockers, Brinkman sensed there was a sort of buddy movie as well in the relationship between Jett and her dad: “Their banter is great, and I thought it would be entertaining for people to see that too.” A documentary wasn’t an easy sell, though, at least to Jett. “She’s an incredibly humble person, and somewhat private,” Brinkman says. “So it was kind of a reluctant getting-on-board.”

It’s oddly hard for Jett to be the center of attention offstage. “I find it very difficult to say, ‘Oh yeah, people are taking notice of me now!’” she says, having been coaxed to say just such a thing. “It just sounds weird and not humble. I find it hard to toot my own horn too loud, unless it’s in conjunction with something else, like the Runaways, or saying ‘the Blackhearts.’ But I can’t talk about me like that.”

So, leave it to her documenters. Kevin Kerslake has been one of the biggest video-directing names ever since he helmed three Nirvana clips in the early ’90s. He signed on at the end of 2016. “That’s not a lot of time to make a doc, especially one that has that kind of historical scope,” Kerslake says. “But we just put the foot to the floor.” He’s an unabashedly admiring chronicler: “I’m a huge punk-rock nut, and her roots tug on that sensibility. I also wanted to get at her stepping outside of the music world and having an impact on social justice and animal rights.” But at the core of it, he, like everyone, was taken by “the arc of a young girl, and then a young woman, cutting a path in a man’s world throughout her entire career, as a sort of feminist manifesto in the flesh.”

Kerslake was fully on board with doing a film that would be more about Jett’s career than her private life. There’s a vintage interview snippet early in “Bad Reputation,” “when she was with the Runaways and was asked about relationships and sex, and she says right then and there — as a teenage girl — that if she got into that, then from that point on every inquiry would really be colored by that answer. So, for me, it was sort of a relief. I don’t care who people sleep with or love as long as they’re doing right in the world. Plus, she’s just a workhorse, so I don’t think there’s a lot of time for relationships, in a way” — a point Jett addresses toward the end of the doc, a bit wistfully but with no great regrets.

There is an on-screen love affair, of sorts, with Laguna. “A lot of people say we’re like a married couple,” says Jett. “Soul mates sounds corny, but it feels right. We definitely connected on a mission. We’re not alike at all, but on some things we totally come together. We push each other’s buttons, and he tests and pushes me, and it’s engaging intellectually as well. It can go from very friendly to explosive and then two seconds later be fine, though it’s probably traumatic for the people around us,” she laughs.

Interviewees in the doc include onetime co-star Fox, Debbie Harry, Iggy Pop and Green Day’s Billie Joe Armstrong. Laura Jane Grace of Against Me! speaks to Jett being one of the first to call and offer support when she came out as transgender. Miley Cyrus talks about finding inspiration in musical lust: “I think there’s this thing that women are supposed to act like we don’t like to f**k too.” Kathleen Hanna touches on Jett’s personal mentorship of members of the riot grrrl generation. Stewart recalls the instruction she got from Jett about how to look more convincing as a rock guitarist: “Pussy to the wood, Kristen!” (“You had to be there” is all Jett will say of this particular inclusion.) And on the other end of the spectrum, there’s a worshipful cameo from unlikely mega-fan U.N. ambassador Nikki Haley.

Jett became a big pop star in the ’80s, of course, but she chuckles at how little that was worth to some. “I learned in the film that Ian MacKaye from Fugazi had no idea who I was,” she says, “but once he knew I was the person that produced the Germs, because that was a big [band] to him, then he knew who I was. It’s just so funny. It’s why you can’t be a smart-ass and assume that everybody knows who you are, because depending on what world you travel in, you might not make a dent. So just be humble and be happy you’re making a living doing what you love.”

Given Jett’s extreme role-model status, the film’s guest list naturally tips to appreciative women. She values the new climate of outspokenness that might make things easier on younger generations. “The situations women and girls find themselves in daily is something I’ve dealt with since before being in a band was even a conscious thought in my head,” she says. “I applaud the women who have found the strength to speak out about demeaning, vicious, sometimes violent experiences and a misogyny that is pretty much baked into American society. In my experience, very little has changed on that plain in 40 years. Now that attention is focused on these entrenched problems, let’s deal with it at its roots and not let this moment slip through our fingers.”

Kerslake tries to tilt the movie’s climax toward Jett’s activism for animals and the environment. But career-wise, there’s another obvious happy ending. In 2014, she’s seen fronting the surviving membership of Nirvana at that band’s Hall of Fame induction, with Krist Novoselic knocking the Hall for not already having her in. The following year, she made it. “Part of me thinks that [Nirvana members] saying it on TV pressured them into it. Krist was saying, ‘What are you guys, nuts?’ So he embarrassed them into it.” She pauses, chuckling. “That’s my humbleness again.”

As it turns out, humility and swagger aren’t mutually exclusive.