Briem is an Icelandic and German surname. Notable people with the surname include: Alexandra Briem (born 1983), Icelandic politician Anita Briem (born 1982), Icelandic actress and screenwriter Elín Briem (1856–1937), Icelandic teacher and author Halldóra Briem (1913–1993), Icelandic architect Helen Briem (born 2005), German golfer Helgi Pálson Briem (1902–1981), Icelandic diplomat (born 1957), German soccer player and trainer Ray Briem (1930–2012), American radio personality Valdimar Briem (1848–1930), Icelandic poet (1841–1912), Austrian composer