The show features Izzard and Driver as Wayne and Dahlia Malloy; they, along with their family, are Irish Traveller con artists and thieves. They travel with their children Di Di (Delilah), Sam and Cael. As the series begins Dahlia has just been paroled from prison. During her two-year sentence, she has developed various drug addictions. In her absence, Wayne and the children have been continuing to act as con artists across the US. After a brief reunion with their Traveller clan, the family flees to avoid an arranged marriage for Di Di, and because Wayne has stolen the clan's hoard of cash. After getting into an altercation and RV chase with another Traveller family, the Malloys are involved in a car accident that kills a very wealthy couple (the eponymous Riches). Choosing not to return to their clan camp, they instead adopt the Riches' identity in suburban Baton Rouge, Louisiana and live as buffers, as they call mundane, law abiding people.