Greta was born in Milan to an Italian art dealer father and an English dancer and art dealer mother on 18 February 1960. Her parents divorced when she was 4 and she returned to her mother's native England. When she was 15, her mother remarried an Italian academic and the family moved to Australia, where Greta took up acting studies in Perth. She continued those studies in the late 1970s back in England at the Bristol Old Vic Theatre School, alongside the likes of Miranda Richardson and Amanda Redman. Being fluent in four languages has allowed her to be more flexible than many actresses.
Her movie debut came in 1982 in the German film Das Zweite Gesicht. She was soon taking leading roles in movies such as Heat And Dust, The Ebony Tower, The Coca-Cola Kid and Country Life. She has continued an acclaimed stage career also, at the same time as turning increasingly to high profile television work in recent years. Greta picked up an Emmy Award for her portrayal of Empress Alexandra Fyodorovna of Russia in the television film, Rasputin: Dark Servant of Destiny. Most recently she has featured in the TV series War & Peace and Versailles. In her personal life, Greta has a son from a past relationship with actor Vincent D'Onofrio.