Released as a download by Radiohead for whatever buyers saw fit to pay, In Rainbows was Radiohead's first album in more than four years. It is also perhaps the band's greatest work. The album's greatest strength is how perfect each song is individually, yet how well the songs fit together to form a cohesive masterpiece. There is no reason to ever skip a track here.

A perfect example of controlled chaos, half of the songs on Wolf Parade's debut full-length are driven by the spastic warble of Spencer Krug, while the other half feature Dan Boeckner's growling croon. Separately, both Krug and Boeckner have proven they can make great albums. But Apologies shows that when they're together, no current indie band does it better.

Funeral hit the indie scene like a bomb in 2004, proving that even in the digital distribution age, an indie band that puts out a debut this brilliant can become a mainstream sensation. Perhaps the most amazing thing about Funeral is that it sounds like nothing else despite being a conventional indie album, with its blend of unique instrumentation and the urgent passion of lead singer Win Butler.

Considered by many to be Radiohead's masterpiece, Kid A was a radical departure from 1997's OK Computer, perhaps the finest album of that decade. The best moments on this album, such as opener "Everything in Its Right Place" and emotional core "How to Disappear Completely" are among the finest songs Radiohead has recorded, but The Top 13 ranked In Rainbows higher for maintaining that brilliance on every track.

It is a rare feat for a band to release back-to-back masterpieces. But that is what Modest Mouse did when it followed the critics' darling The Lonesome Crowded West with this album, a moody, dark, and epic step forward for Modest Mouse. Pitchfork was effusive: "For at least a few months, the world can stop waiting for Radiohead's next album, and start wondering how in the hell Modest Mouse will ever top the monumental, ground-breaking, hypnotic, sublime The Moon & Antarctica."

Return to Cookie Mountain is an album driven by unique vocals – from Tunde Adebimpe’s fantastic bellowing yelps to guitarist Kyp Malone’s haunting falsetto to memorable guest vocals from David Bowie (on "Province") and Kazu Makino of Blonde Redhead (on "Hours"). But it's TV on the Radio’s mesmerizing instrumentation and looping that turn Cookie Mountain into a one-of-kind rock album that successfully merges touches of shoegaze, funk, prog, neo-psychadelia, and more.

For those who loved Portishead’s first two albums, Third can be jarring. While the haunting chanteuse voice of Beth Gibbons provides a reminder of the work the band did on its classic Dummy, most of this album veers into less familiar territory. The songs are generally faster, less balanced, more urgent, and more psychedelic than anything else Portishead has done. Nevertheless, Third is a terrific album, which with the benefit of time likely will be considered every bit as influential as the band’s earlier work.

You will never hear a band sound more vulnerable than this. YHF was conceived out of a total artistic breakup - among band members, with the band's record label - and overflows with deeply felt love and regret. Back-to-back standouts "Jesus, Etc." and "Ashes of American Flags" are possibly the two best songs of Wilco's storied career.

Nothing released by Ben Bridwell's prior band, Carissa's Wierd, signaled what was to come with Everything All the Time. Indeed, where that band made slow, layered heartbreaking tracks, this album is a raucous, countrified indie rock album that sounds like something Neil Young would release if he was still creating innovative music.

Source Tags is a nearly perfect hard-rock album, so much so that it's impossible to figure out either how this band pulled it off in the first place or why they haven't come close on any album since. Whatever the reason, this one's for the ages, and it rocks.

Here is the modern take on the concept album. Black Sheep Boy adopts the protagonist from Tim Hardin’s song of the same name, Okkervil’s cover of which opens the album, and then uses him as narrator for the remaining songs. The album is filled with emotional and desperate country-tinged songs about failed love, and Okkervil uses an expanded lineup and a battery of instruments to complement the pain-filled lyrics with fantastic hooks.

It’s not an overstatement to say that Supreme Clientele saved the Wu-Tang Clan. After a series of middling solo releases from various Clan members, Ghostface emerged from a stint at Rikers Island to reignite the Wu. The production on Supreme Clientele - featuring RZA and several other producers is typically fantastic – but it is Ghostface’s amazing versatility on the mic that makes this The Top 13’s favorite hip hop album of the decade.

Produced by Dave Sitek from TV on the Radio (another band with an album on this list), Fever to Tell is the Yeah Yeah Yeah's debut full-length release. Although the album is best known for the sing-a-long ballad "Maps," the rest of the album is full of confrontational art rock tunes featuring the banshee voice of Karen O. The album was an ode to New York's punk scene of a generation earlier, but at the same time signaled a resurgence of that city's indie rock scene.