Their Greatest Hits (1971–1975) is a singles compilation album by the Eagles, released in 1976. As of November 2012, 29 million copies have been shipped in the domestic market, making it tied with Michael Jackson's Thriller as the best-selling album in the United States. With an additional 13 million internationally, for a total of 42 million, it is one of the top-selling albums in music history.

Their Greatest Hits (1971–1975) comprises ten best-selling singles released between 1972 and 1975, as well as "Desperado", which had never been previously released as an A-side. All single tracks but "Tequila Sunrise" charted in the top 40, with five in the top ten, and "One of These Nights" and "Best of My Love" both topping the singles chart. With such airplay success in the span of a little over four years, the band became a formidable presence on American commercial radio in the 1970s, and Their Greatest Hits (1971–1975) debuted at number four on the Billboard 200 album chart upon its release and later peaked at number 1.