"Their Greatest Hits (1971–1975)" is the first compilation album by the American rock band the Eagles, released on February 17, 1976, by Asylum Records. This album features a curated selection of tracks from the band’s first four studio albums, which were released between 1972 and 1975.
The album achieved significant success, reaching number one on the U.S. Billboard 200 chart and remaining in that position for five consecutive weeks. Notably, it was the first album to be certified platinum by the Recording Industry Association of America (RIAA), a new certification introduced in 1976 for albums shipping over one million copies in the United States.
 
Their Greatest Hits (1971–1975) was ranked number four on Billboard’s year-end album chart for 1976 and has spent a remarkable 422 weeks on the Billboard 200 as of September 2023. The RIAA has certified the album 38 times platinum, reflecting sales of 38 million copies in the U.S., making it the best-selling album of the 20th century in America. Although Michael Jackson’s Thriller surpassed it in platinum certifications posthumously in 2009, Their Greatest Hits (1971–1975) regained the top spot in August 2018. In 2017, the album was inducted into the Library of Congress's National Recording Registry for being “culturally, historically, or aesthetically significant.”