In a mesmerizing video from 1988, Björk, the Icelandic musician and diminutive sprite, dismantles a clunky television and sensuously declares its knobs, chips, and cables to be “like a little model of a city,” with “houses, streets, and an elevator.” At the time, she was in her early twenties and a singer for the post-punk band The Sugarcubes. Her iconoclastic demeanor, however, was already in full effect.

Her voice childlike and otherworldly, as if narrating a fairy tale, she explains that an Icelandic poet had claimed TV would “hypnotize” her. With a grin, she said she was relieved to learn “the scientifical truth” from a Danish book: “You shouldn’t let poets lie to you.”

The magic pixie caricature persists for Björk, who is now 49. But nowadays it’s more closely linked to her inventive music than the swan she wrapped around her neck at the 2001 Oscars.

Since 1993, Björk has recorded seven studio albums, each one more innovative and ambitious than the last. From her early electro-pop hits on Debut and Post to the app she created for her interactive 2011 album, Biophilia, Björk’s success, stardom, and critical adulation has endured over two decades.

Now, timed with the release of her latest album, Vulnicura, the Museum of Modern Art in New York City is honoring Björk’s career as a musician, composer, and multimedia artist with a retrospective exhibit that will surely be the most talked-about show at MoMA since Christian Marclay’s The Clock.

There was predictable chaos at Tuesday’s preview for press and VIPs, who were already queuing up at 9 a.m. for Songlines, an interactive audio tour through Björk’s albums. Outside the installation, they watched a selection of her live performances projected on flatscreen TVs from MTV Unplugged in 1994 to Vespertine Live at the Royal Opera House in 2002.

The 40-minute, labyrinthine audio tour that follows is an idiosyncratic and mostly fictitious biography called The Triumphs of a Heart, written by Icelandic poet Sjón and narrated by Margret Vilhjalmsdottir, an Icelandic actress. (Both are longtime friends of Björk.) Punctuated with her songs, it’s a musical and narrative journey with corresponding visuals from Björk’s life and career. We hear “Venus as a Boy” from Debut, the lyrics of which are scribbled in one of her many diaries on display, some from when she was as young as 9.

The installation includes props from music videos, like the robots featured in “All Is Full of Love”; the many faces and phases of Björk, all painted, glued, and sewn on a slew of masks and life-size mannequins that show just how tiny she is (they were 3D scanned from her body).

One Björk mannequin wears her infamous Oscars swan dress; another smiles through the massive body sculpture worn during her zany Volta tour; another is weighed down beneath a red afro wig and voluminous blue Iris van Herpen dress from the Biofilia tour. Björk’s ex-husband Matthew Barney helped assemble her nipple piercing, pearl-and-lace wedding gown, designed by the late Alexander McQueen for her “Pagan Poetry” music video. The dress is draped over a rotating, translucent plastic figure in one of the show’s most haunting pieces.

After Songlines, visitors waited in another line to see the exhibition’s piece de resistance: the MoMA-commissioned video installation for “Black Lake,” a 10-minute song about Björk’s divorce from Barney from her latest record.

After seeing Björk everywhere on Tuesday morning, some were disappointed that the artist was so elusive when she appeared in the flesh beside Klaus Biesenbach, MoMA’s curator-at-large who helped conceive the retrospective. (He first approached her in 2000, but it would be 12 years before she took up the offer.) Standing in the darkness, Biesenbach and Björk said a few words to some 100 visitors before slipping out the back. “You can’t even see her!” one exasperated woman whispered behind me.

“‘Black Lake’ is a very transformative piece,” Biesenbach said later at a well-lit press conference, which Björk did not attend. “We spent last summer in a cave in Iceland, and for nearly three days Björk was barefoot in a dress made out of copper wire,” he said of the video. “We were all completely exhausted. Not she.”

The space where “Black Lake” is installed is similarly cavernous, its ceiling lined with thousands of soundproofing cones. Architect David Benjamin worked with sound engineers to design a 3D topography, using the song as a blueprint so that sounds reverberate uniquely from every inch of the room.

“From the very beginning, Björk had this concept of sound lines—of a topography being understood as a song in a landscape,” said Biesenbach. “She wanted to make an exhibition where music is an authentic experience in a museum, like a painting is an authentic experience.”

When they began working on the exhibition three years ago, Biesenbach said he knew Björk wouldn’t be invested in a project that heavily emphasized looking backward like most retrospectives. “So I told her to think about your retrospective looking back at your career but also about where you will have arrived in three years. I think that caught her interest.”

Much like the 1988 video of Björk explaining television, the MoMA retrospective merges her lyrical sensibilities with technological innovation. It looks back and forward at the same time, and this is what makes Björk so enigmatic.

Her influence as an artist lies in tempering the unfamiliar with palatable nostalgia—and refusing to sacrifice emotional or musical purity in being avant-garde.