Their Greatest Hits (1971–1975) is the first compilation album by the American rock band the Eagles, released by Asylum Records on February 17, 1976.

[1] The RIAA has certified the album 38 times platinum, indicating sales of 38 million copies in America alone, which would make Their Greatest Hits (1971–1975) the best-selling album of the 20th century in the United States (it was surpassed in platinum certifications by Michael Jackson's Thriller after Jackson's death in 2009,[2] but regained the title in August 2018).

In 2017, the album was selected by the Library of Congress for preservation in the National Recording Registry as being "culturally, historically, or aesthetically significant".

[6] Don Henley was unhappy that songs like "Tequila Sunrise" and "Desperado" were lifted out of the context of the original album in a way that he thought was detrimental to the nature, quality, and meaning of the music.

[8] The piece consists of a painted plastic cast of an eagle skull[9] against a light-blue background made of silver mylar.

The bumpy appearance of the background gave rise to a myth that it was covered in cocaine powder that the band snorted after the photo shoot.

The band chose not to debunk that myth, though Glenn Frey reportedly also noticed the resemblance and told Elder that the background reminded him of "a field of blow" (a slang term for cocaine).

William Ruhlmann of AllMusic said the songs in the compilation are melodic, immediately engaging, and lyrically consistent, so, "unlike the albums from which they come, these songs make up a collection consistent in mood and identity, which may help explain why Their Greatest Hits (1971–1975) works so much better than the band's previous discs and practically makes them redundant.

Warner Music, which distributed Their Greatest Hits, claimed the figure came from newly discovered sales dating back to 1976, but a representative from Michael Jackson's estate noted sales audits are usually restricted to three years and said, "The notion that they can go back 10, 15, 20 or 30 years and find units that were never counted before is absurd, they reviewed these records before.