- Fluent in five languages French, Danish, English, Swedish and Italian.
- Has written three novels.
- Made 8 movies with ex-husband Jean-Luc Godard: Vivre sa vie (1962), A Woman Is a Woman (1961), The Oldest Profession (1967), Pierrot le fou (1965), The Little Soldier (1963), Made in U.S.A (1966), Band of Outsiders (1964) and Alphaville (1965).
- Thought then-husband Jean-Luc Godard made her look ugly on Vivre sa vie (1962).
- In the 1980s, she lived in Los Angles for a while where she met her fourth husband, Dennis Berry.
- Coco Chanel chose her pseudonym.
- Appeared in a short film when she was 14, which later won a prize at the Cannes Film Festival.
- Companion of Ulli Lommel in the late 1970s. The couple made few movies together, including Rainer Werner Fassbinder 's Chinese Roulette (1976) and Ausgerechnet Bananen (1978), directed by Lommel.
- Studied dance and painting in Denmark.
- Used to play the piano.
- At 17 she worked as a photographic model.
- When she arrived in Paris she lived in a rented small room in the Bastille area.
- Friends with Jean-Claude Brialy and Jean-Paul Belmondo.
- Husband Dennis Berry was once married to Jean Seberg (1972-1978) whom Anna's first husband, Jean-Luc Godard, directed in Breathless (1960) (aka Breathless).
- Recorded the soundtrack album for her TV musical film Anna (1967) with songs written by Serge Gainsbourg and accompanied by her co-star and friend Jean-Claude Brialy on the vocals in a couple of songs.
- Member of the jury at the Montreal International Film Festival in 2005.
- Daughter-in-law of John Berry.
- Daughter of Carl Johan Christoph Bayer, a police officer, and Elva Helvig Bayer, née Frederiksen.
- Has worked with film directors such as Agnès Varda, Roger Vadim, Valerio Zurlini, Jacques Rivette, George Stevens, Volker Schlöndorff, George Cukor and Rainer Werner Fassbinder.
- In 1972 set up a production company named Raska.
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