Norén is considered Sweden's most prominent contemporary playwright of today. He wrote his first play at age 19. His first publication was a collection of poems - Syrener, snö (Lilac, snow) in 1963. His plays are realistic and often revolve around family relations and the impoverished and routed at the bottom of society. Norén became well known in connection with the murders of two policemen in Malexander in 1999. The culprits had received furlough from their incarceration at Österåker jail to participate in Norén's play 7:3. In 1971 he received Aftonbladet's literary prize.