Roberts' big break came in 1998, when she appeared in Solomon a Gaenor opposite Ioan Gruffudd. With dialogue in Welsh and Yiddish, the movie won Best Film at the 2000 Verona Film Festival and was nominated for Best Foreign Language Film at the 72nd Academy Awards.

Her subsequent Welsh-language credits include Fondue, Rhyw a Deinosors!, Newes of the Weeke, Y Palmant Aur, Glan Hafren, the long-running soap opera Pobol y Cwm, and S4C's gangster drama Y Pris. Roberts' English-language television credits include the comedy series Dr. Terrible's House of Horrible, the drama Border Café, and several single-episode appearances in prime-time British shows such as The Bill and Casualty. Roberts has starred in two films directed by her husband, Marc Evans: Snow Cake (2006), a drama focused on the friendship between a high-functioning autistic woman and a man who is traumatized after a fatal car accident; and Patagonia (2009), a drama set in Y Wladfa, Argentina. In 2009, Roberts also starred as registrar Mary Finch in Crash!, a hospital drama commissioned by BBC Wales and produced by Tony Jordan. In 2010, Roberts guest-starred in the two-part Doctor Who Series 5 episode The Hungry Earth/Cold Blood. More big-screen productions followed: She appeared in Hattie Dalton's Third Star (2010) and in Vertigo Films' The Facility (2012), an atmospheric, micro-budget horror film about volunteers fighting for their lives after a drug trial goes wrong. In 2014, Roberts appeared in the fourth episode of Y Gwyll (Hinterland), a highly acclaimed noir detective series shot in both Welsh and English.