Björk further promoted the album by performing the song "Oceania" at the 2004 Summer Olympics opening ceremony, Friday Night with Jonathan Ross and other television and radio shows.

Other than these few performances, no concerts or tours were arranged to promote Medúlla, as Björk thought it would be too difficult to play the songs live.

[4] In an interview with The New Yorker, she explained that she wanted to get away from the world of instruments and electronics present on her previous album, Vespertine (2001), and remarked that the project was "very introverted" and avoided eye contact.

[6] Björk began working on the album while eight months pregnant by adding her own live drumming to the arrangements of previously recorded demos.

[6] However, the "musical fascist" in her decided using any MCs or vocal percussionists would be too "cheesy"; she later changed her mind when she saw beatboxer Rahzel from The Roots freestyle a whole Kraftwerk track without pausing for breath.

"[5] The album cover for Medúlla was photographed by duo Inez van Lamsweerde and Vinoodh Matadin in London, on 28 June 2004, and designed by M/M Paris.

[14] Van Lamsweerde said that they "were all inspired by women's handicrafts and this idea of being in your own cocoon in your home, with your family, and this reclusive character that hand-makes the whole world around her".

[15] In an interview with Style magazine, Shoplifter talked about her part at the exhibition, explaining that it dedicated a room to each album of Björk's career, with the Medúlla section having a mannequin wearing the hairmask and the dress designed by Alexander McQueen which she wore in the music video for "Who Is It".

She provisionally called it Ink, a title that suggested to her the idea of "that black, 5,000-year-old blood that's inside us all; an ancient spirit that's passionate and dark and survives.

At the time of its construction, Björk considered Medúlla to be her most political album, saying that it countered outbreaks of racism and patriotism that followed the 11 September attacks.

[21] Regarding the album's composition, Björk also mentioned that she tried to find the common soul in everything, outside nationality and religion, whilst elaborating that she felt that "in that sense, it's a greatest hits of human spiritualism [laughs].

[28] The publication also added: "The electronic treatments range from industrial distortion to percussive glitches and dreamy layering, rarely descending into novelty".

[28] The album combines beatboxing, classical choirs that suggest composers like Penderecki or Arvo Pärt, and "mews, moans, counterpoint and guttural grunts" provided by herself and guests like Mike Patton, Robert Wyatt and Tanya Tagaq.

[29] Medúlla includes "vocal fantasias" that lean toward chamber music, alongside tracks that "are obviously but distantly connected to hip-hop.

"[29] Glimpses of Bulgarian women's choirs, the polyphony of central African pygmies, and the "primal vocalisms" of Meredith Monk were also noted.

[29] The album opens with "Pleasure Is All Mine", which begins with a vocal harmony layered on top of a woman's panting for a short while prior to when Björk starts singing her verses.

The echo effects in "Who Is It" may additionally reflect the scattered sense of self the mother may experience as she carries the burden of constant care for her child.

[36] "Submarine", the seventh track on the album, was influenced by Björk's pregnancy with her daughter Ísadóra and how she felt somewhat lazy during that time.

[17][20] It has a "hint of political consciousness", and features the "reedy" voice of singer Robert Wyatt multiplied into a chorus to share lines like "Shake us out of the heavy deep sleep, do it now".

[29] The next track "Desired Constellation" was created from a sample of Björk singing the phrase "I'm not sure what to do with it" from "Hidden Place" on her previous album, Vespertine.

[38] Tenth song "Sonnets/Unrealities XI" was based on the poem "It May Not Always Be So; And I Say" by E. E. Cummings, and features only Björk's singing, with small inflections from the Icelandic Choir[34] while she bids farewell to a lover lyrically.

[29][34] On the thirteenth track of the album, "Miðvikudags", Björk sings once again in gibberish, while some "doot-doos" can be heard in the background, reminiscent of "Öll Birtan".

The song also features orchestral arrangements by the Icelandic and London Choirs,[41] as well as hooks coming from a "human trombone", herself, Gregory Purnhagen, and Rahzel and Dokaka.

She wore a very large dress which unfolded during her performance to eventually occupy the entire stadium and showed a map of the world in sign of union.

[52] On 10 October 2004, Björk performed a set of five songs live in studio for Gilles Peterson's BBC Radio 1 program.

[53] On 25 October 2004, Björk performed a set of six songs for the French television show Album de la Semaine at Canal+ studios in Paris, France.

[60] Dominique Leone from Pitchfork commented that Medúlla was "an interesting record", while saying Björk had "found a way to bathe her immediately distinctive melodies and vocal nuances in solutions that cause me to reevaluate her voice and her craft".

also gave it a positive review, saying "pairing gooey purrs with grooves provided by a human trombone might not seem like a good idea, but when Björk is the one making the arrangements the effect is spine tingling".

[38] Heather Phares of AllMusic thought that Medúlla was "not an immediate album, but it is a fascinating one, especially for anyone interested in the world's oldest instrument being used in unexpected ways".

[71] Björk received two Grammy Award nominations for Medúlla, including Best Female Pop Vocal Performance for "Oceania", and Best Alternative Music Album.