"Given Up", along with "No More Sorrow" and the hit single "What I've Done", made its live debut on April 28, 2007 in Berlin, Germany. Live performances of these three songs at the AOL sessions were released on AOL on May 5, 2007. The performance of the song is available on the "Bleed It Out" single.
"Given Up" is the heaviest song on the album. It notably features a seventeen second-long scream by Chester Bennington before the final chorus, as well as a steady guitar riff for the choruses of the song. The scream is often split into two 9 second long screams when performed live allowing Bennington to catch his breath, although he has completed the full scream in various live performances. It dawns a distinctive jingle sound during the verses and intro, generated by the jingling of guitarist Brad Delson's ring of keys and a steady clapping beat by Mike Shinoda. It also contains the second most amount of profanity of any Linkin Park song (the most being "When They Come For Me", a song from the band's fourth album, A Thousand Suns) with the word "fuck" being featured in the chorus and the bridge. The song was made available as a single on March 3, 2008. It is included as a master track in the Xbox 360, PlayStation 3, and NintendoWii versions of the music video gameRock Revolution, though this version is heavily censored. The song was also used in the trailer and commercials for the action film Crank 2: High Voltage, in which Bennington makes a cameo.
In June 2007, the official Billboard website gave information stating that "Given Up" and "Shadow of the Day" would be the next two singles from Minutes to Midnight, following "What I've Done". This proved incorrect after "Bleed It Out" was promoted to single status, and by that time, was released as a promo single between "What I've Done" and "Bleed It Out" mainly due to heavy airplay on alternative rock stations at the time. On January 24, 2008, it was announced that "Given Up" would be the band's next single after "Shadow of the Day", released on October 16, 2007. The single was released as digital download on February 17, 2008 along with a cover art.
On Chester Bennington's official blog, he stated when the video was being shot and that it features live performance from the band. Bennington told the crowd at the MEN Arena and the O2 Arena during shows on January 27 and 29 that the performance of "Given Up" was recorded for use in the video, although cameras were also visible during the performance of the song at the concert on January 28 at the O2 Arena. Linkin Park had officially finished filming the video on February 6, according to Billboard. The video premiered on the band's official website on March 3, 2008 at 4p.m. Pacific Standard Time (Midnight UTC). The video was uploaded to the band's YouTube channel on March 4, 2008. The video was directed by Mark Fiore, the band's videographer.
The video consists of live clips from the shows (stated above) and has been edited together in a sharp, rugged manner which contains short cut scenes with many special effects, mainly altering the coloring. Transitions between cut scenes are in a style of worn analog tape distortion giving the video an even more rugged, tough appearance. Bennington performs his seventeen-second scream perched on the guard rail, inches from the audience. Throughout the video, several flash scenes appear such as a cowboy, hippopotamus and quotes from "Magical Thinking: True Stories" (chapter "Commercial Break") a book by the Augusten Burroughs. Frames from the Linkin Park videos "One Step Closer", "Papercut", "What I've Done", "Numb", and "Breaking the Habit" can also be seen throughout the video.
"Given Up" was the least successful single of Minutes to Midnight. The single charted on Billboard's Hot 100 and Pop 100 charts at numbers 99 and 78 respectively in May 2007, following Minutes to Midnight's release. Following the singles official release, the song debuted at #34 on the Mainstream Rock Tracks, peaking at #5. It also debuted at #32 on the Modern Rock Tracks, peaking at #4.