Björk's preferred studio mic. Her vocal on "Unravel" was recorded with an SM58, according to a Waves webinar with producer & co-writer Guy Sigsworth (at 37:45):

I have even made really popular records with SM58s. Björk's vocals on "Unravel" are SM58, and they were just great performances, didn't mind about the mic.

In this October 13, 2011 SonicScoop interview with mix engineer Damian Taylor, he mentions that Björk also used an SM58 for Volta and Biophilia.

One thing that remains consistent, however, was Björk’s method of recording vocal takes. Taylor says she’s not one to stand perfectly still with headphones on. Instead, she’s favored a handheld Shure SM58 for years, and she still tracks all of her vocals while listening out-loud on studio monitors.

When Taylor brought her a Neumann KMS 150 handheld condenser to try, he says that she “sang all of two syllables into it” before handing it back for the 58.

On a few songs that needed extra sensitivity and detail, Björk sang into Martin Kantola and Bruce Swedien designed NU-47, a classic redesign of the U47 with striking wooden body. Otherwise the chain was simple: The Shure SM58 into a preamp with little or no compression.

“When I’m recording Björk, I try to compress as little as possible. Basically never. I do have a little something there on the chain just as a safety net, but basically I ride her performances the whole way in. Her dynamic range is just insane. Fortunately, I’ve gotten to know her pretty well, so I can start to feel when she’s about to take a breath and ride my output gain knob. This way, we’re not getting a squished sound going in, but we’re still getting consistent levels.”

(...) Originally, Taylor plugged the SM58 into a Neve 1084, with a Urei 1176 as his safety net. “That worked really well for Volta, where the voice had a more rock and roll sound.” But for this record, he realized the voice “would be a more delicate kind of thing”, and he came to prefer Björk’s Focusrite ISA 430 Producer Pack, while largely avoiding its built-in EQ and compression.

The Yamaha QY20 is seen in this video about Björk's 1994 studio, starting 0:10

The Yamaha SU10 is seen in The South Bank Show’s 1997 documentary on Björk, starting 37:20:

I used to work quite a lot with QY20. That’s a different machine but same size and you have 8 tracks and 100 noises and you can make as many songs as you want and a lot of my tunes for the last 4 years I wrote on that. It’s so incredibly convenient. You put the batteries in and you can write on the airplane or your grand’s house or the top of a volcano or in a club or in a tube and this is a different machine this is like a sampler. Mark Bell bought this one and he’s just teaching me it.

In the article Bjork states "I play my string arrangements on the keyboard or in Sibelius, but more and more I am using Melodyne to do complex arrangements with my voice. I will then copy those arrangements over to the strings.”

The Casio SA-10 is seen in this video about Björk's 1994 studio, starting 0:10

Used for vocals on Homogenic, as stated by producer Markus Dravs in this October 6, 2008 Audio Pro International interview (as transcribed on the Brian Eno fansite Brian Eno is MORE DARK THAN SHARK).

Dravs explains that her vocals are often recorded in a very simple fashion. "A lot of times, Björk would listen to an almost finished mix and then pick-up a Shure SM57 mic in the control-room, with the speakers on (with a bit of Urei compression on) and re-sing the lead vocal in order to adjust her singing dynamic to what she's hearing at that point and then lay down a blinding performance, as she has got such great mic technique," Dravs reveals.

In the song "Violently Happy," Björk incorporates the Roland D-50 synthesizer, first heard at 0:37 with the "Machine Run" patch. This is demonstrated in the YouTube video "Bjork - Crying" by Cruise Control.

Much of the writing and recording of Vulnicura took place at Björk’s New York home, where she has the ultimate 21st Century studio. The total music–tech content consists of an Avid Pro Tools HD Native Thunderbolt system, Genelec 1032 monitors (“I like them a lot, they sound very creamy. But they can be deceptive, because everything sounds good in them. So you have to be a little careful.”), an M–Audio controller, a Telefunken ELAM 251 microphone and Neve 1081 mic preamp.

During her DJ set at Carriageworks, Björk is seen using Apple Logic Pro X, as captured in a user-uploaded photo.

The Tascam 464 is seen in this video about Björk's 1994 studio, starting 0:10

A Roland TR-909 can be seen as part of Björk's home studio in Spain in this video at 30:26.

Used for Biophilia "[o]n a few songs that needed extra sensitivity and detail," as stated by mix engineer Damian Taylor in this October 13, 2011 SonicScoop interview.

On a few songs that needed extra sensitivity and detail, Björk sang into Martin Kantola designed NU-47, a classic redesign of the Neumann / Telefunken U47 with striking wooden body. Otherwise the chain was simple: The Shure SM58 into a preamp with little or no compression.

“When I’m recording Björk, I try to compress as little as possible. Basically never. I do have a little something there on the chain just as a safety net, but basically I ride her performances the whole way in. Her dynamic range is just insane. Fortunately, I’ve gotten to know her pretty well, so I can start to feel when she’s about to take a breath and ride my output gain knob. This way, we’re not getting a squished sound going in, but we’re still getting consistent levels.”

(...) Originally, Taylor plugged the SM58 into a Neve 1084, with a Urei 1176 as his safety net. “That worked really well for Volta, where the voice had a more rock and roll sound.” But for this record, he realized the voice “would be a more delicate kind of thing”, and he came to prefer Björk’s Focusrite ISA 430 Producer Pack, while largely avoiding its built-in EQ and compression.

Producer Bruce Swedien confirms Björk's use of the NU-47 on this page of the microphone's official website.

Of course, it's a fantastic vocal microphone. There have been very few NU-47's made. One was made for Icelandic singer Björk, who absolutely loves the sound of this incredible new microphone. She told us that, "It captures both the small and the big sounds that I make!"

https://www.youtube.com/watch?v=iQvhjqbaT9E

https://www.nu47.com/NU-47C.pdf

"Damian Taylor employed Max to create alternative creative environments for Björk to conjure within"

In this photo of Björk you can see that she is playing a black Gibson ES-335

She has never really played traditional instruments very much, “which is why I was so excited about the laptop in 1999. I learned to use Sibelius in that year, and most of Vespertine was done on Sibelius — all the music boxes, harps, glockenspiels, and so on. It was the same with ‘Ambergris March’ [from Drawing Restraint 9, a soundtrack album she made in 2005 with Matthew Barney]."

In this photo of Björk you can see that she is playing a Fender Electric XII

"With Vespertine [2001] I recorded all sorts of noises around the house, very quiet ones, and I then magnified them up in Pro Tools, and created rhythms with them. It took me like three years, very enjoyable, but it was like crocheting a huge blanket with a tiny needle." - Björk interview by Paul Tingen

Much of the writing and recording of Vulnicura took place at Björk’s New York home, where she has the ultimate 21st Century studio. The total music–tech content consists of an Avid Pro Tools HD Native Thunderbolt system, Genelec 1032 monitors (“I like them a lot, they sound very creamy. But they can be deceptive, because everything sounds good in them. So you have to be a little careful.”), an M–Audio controller, a Telefunken ELAM 251 microphone and Neve 1081 mic preamp.

These headphones can be seen as part of Björk's home studio in Spain in this video at 30:26, 42:00 and so on.

Much of the writing and recording of Vulnicura took place at Björk’s New York home, where she has the ultimate 21st Century studio. The total music–tech content consists of an Avid Pro Tools HD Native Thunderbolt system, Genelec 1032 monitors (“I like them a lot, they sound very creamy. But they can be deceptive, because everything sounds good in them. So you have to be a little careful.”), an M–Audio controller, a Telefunken ELAM 251 microphone and Neve 1081 mic preamp.

Used for Biophilia, as stated by mix engineer Damian Taylor in this October 13, 2011 SonicScoop interview. Despite being unspecified in the text, this picture is shown.

Instead of relying on conventional instruments to write the songs for the album, Taylor worked within Björk’s specifications to create a suite of unique virtual instruments in Max/MSP that she could then manipulate with a variety of unusual devices while singing.

In place of a traditional instrument or sampler, she would be able to trigger and manipulate her sounds with a Logitech videogame controller, the Telsa-esque tabletop Reactable system, or a first-generation multi-touch screen called the JazzMutant Lemur.

“I think the simplest way to describe what this system allowed her to do, is that there’s no way you could have written these songs on a piano. Compositionally, it allows you to form your ideas and control them very precisely – but in a way that’s completely different from what I’ve experienced playing any other instrument.”

in this video at 30:37, Björk can be seen at her Spanish home studio using her Tascam DA-60 DAT recorder.

Used for vocals on Biophilia, as stated by mix engineer Damian Taylor in this October 13, 2011 SonicScoop interview.

“When I’m recording Björk, I try to compress as little as possible. Basically never. I do have a little something there on the chain just as a safety net, but basically I ride her performances the whole way in. Her dynamic range is just insane. Fortunately, I’ve gotten to know her pretty well, so I can start to feel when she’s about to take a breath and ride my output gain knob. This way, we’re not getting a squished sound going in, but we’re still getting consistent levels.”

(...) Originally, Taylor plugged the SM58 into a Neve 1084, with a Urei 1176 as his safety net. “That worked really well for Volta, where the voice had a more rock and roll sound.” But for this record, he realized the voice “would be a more delicate kind of thing”, and he came to prefer Björk’s Focusrite ISA 430 Producer Pack, while largely avoiding its built-in EQ and compression.

Used for vocals on Volta and (initially) Biophilia, as stated by mix engineer Damian Taylor in this October 13, 2011 SonicScoop interview.

“When I’m recording Björk, I try to compress as little as possible. Basically never. I do have a little something there on the chain just as a safety net, but basically I ride her performances the whole way in. Her dynamic range is just insane. Fortunately, I’ve gotten to know her pretty well, so I can start to feel when she’s about to take a breath and ride my output gain knob. This way, we’re not getting a squished sound going in, but we’re still getting consistent levels.”

(...) Originally, Taylor plugged the SM58 into a Neve 1084, with a Urei 1176 as his safety net. “That worked really well for Volta, where the voice had a more rock and roll sound.” But for this record, he realized the voice “would be a more delicate kind of thing”, and he came to prefer Björk’s Focusrite ISA 430 Producer Pack, while largely avoiding its built-in EQ and compression.

Used for Biophilia, as stated by mix engineer Damian Taylor in this October 13, 2011 SonicScoop interview.

Instead of relying on conventional instruments to write the songs for the album, Taylor worked within Björk’s specifications to create a suite of unique virtual instruments in Max/MSP that she could then manipulate with a variety of unusual devices while singing.

In place of a traditional instrument or sampler, she would be able to trigger and manipulate her sounds with a Logitech videogame controller, the Telsa-esque tabletop Reactable system, or a first-generation multi-touch screen called the JazzMutant Lemur.

“I think the simplest way to describe what this system allowed her to do, is that there’s no way you could have written these songs on a piano. Compositionally, it allows you to form your ideas and control them very precisely – but in a way that’s completely different from what I’ve experienced playing any other instrument.”

Used for Biophilia, as stated by mix engineer Damian Taylor in this October 13, 2011 SonicScoop interview. She had previously incorporated it into her tour for Volta.

Instead of relying on conventional instruments to write the songs for the album, Taylor worked within Björk’s specifications to create a suite of unique virtual instruments in Max/MSP that she could then manipulate with a variety of unusual devices while singing.

In place of a traditional instrument or sampler, she would be able to trigger and manipulate her sounds with a Logitech videogame controller, the Telsa-esque tabletop Reactable system, or a first-generation multi-touch screen called the JazzMutant Lemur.

“I think the simplest way to describe what this system allowed her to do, is that there’s no way you could have written these songs on a piano. Compositionally, it allows you to form your ideas and control them very precisely – but in a way that’s completely different from what I’ve experienced playing any other instrument.”

Used for vocals on Volta and (initially) Biophilia, as stated by mix engineer Damian Taylor in this October 13, 2011 SonicScoop interview.

“When I’m recording Björk, I try to compress as little as possible. Basically never. I do have a little something there on the chain just as a safety net, but basically I ride her performances the whole way in. Her dynamic range is just insane. Fortunately, I’ve gotten to know her pretty well, so I can start to feel when she’s about to take a breath and ride my output gain knob. This way, we’re not getting a squished sound going in, but we’re still getting consistent levels.”

(...) Originally, Taylor plugged the SM58 into a Neve 1084, with a Urei 1176 as his safety net. “That worked really well for Volta, where the voice had a more rock and roll sound.” But for this record, he realized the voice “would be a more delicate kind of thing”, and he came to prefer Björk’s Focusrite ISA 430 Producer Pack, while largely avoiding its built-in EQ and compression.

In a highly publicized new interview on Salon.com, Brian Eno asserted that 'success ruins artists.' I beg to differ, especially after hearing the new Björk album Biophila and interviewing her engineer and Music Director Damian Taylor. Björk has used her success to collaborate, push boundaries and reach new heights in experimentation. Among other things, Damian employed Max to create alternative creative environments for Björk to conjure within.

In this photo from 1995, Björk can be seen playing a Hohner Alto Melodica