Mark was born and brought up in west Wales before moving to Cardiff more than 30 years ago. A former probation officer, youth justice worker and Barnardos project leader in Ely and Caerau, he has been a professor of Social Policy and Applied Social Sciences at Cardiff University. In the 1980s and 1990s Mark was a Labour Councillor on South Glamorgan County Council. Between 2000 and 2010 he worked as the Cabinet's health and social policy adviser at the Welsh Government.

Mark became the Assembly Member for Cardiff West in May 2011, and was re-elected in May 2016. In December 2018 Mark was elected Leader of Welsh Labour.