Enyedi's film On Body and Soul premiered at the 67th Berlin International Film Festival, where it won the Golden Bear. The film went on to be nominated for the Academy Award for Best Foreign Language Film representing Hungary.
She won the Golden Camera award for Az én XX. századom at the 1989 Cannes Film Festival. In 1992 she was a member of the jury at the 42nd Berlin International Film Festival. Her 1994 film Magic Hunter was entered into the main competition at the 51st edition of the Venice Film Festival. In 2007 she was a member of the jury at the 29th Moscow International Film Festival.
In 2018 she announced her next film would be an adaptation of The Story of My Wife, about a man who makes a bet with his friend to marry the next woman who walks into the café where they are eating. The film was adapted from a novel by Milán Füst of the same name.
