Eagles: Their Greatest Hits 1971-1975 (Vinyl LP)

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. It contains a selection of songs from the band's first four albums, which were released from 1972 to 1975. On the U.S. Billboard 200 chart, the album reached number one, where it stayed for five weeks.

The album has the distinction of being the first album to receive the RIAA's Platinum certification, which was introduced in 1976 to recognise albums that ship one million copies in the United States. It was ranked number four on Billboard's year-end album chart for 1976, and has spent a total of 239 weeks on the Billboard 200 (as of August 2018).

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, 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 artistically significant".