Unhealthy food and non-alcoholic beverage marketing (UFM) adversely impacts children's selection and intake of foods and beverages, undermining parents' efforts to promote healthy eating. Parents' support for restrictions on children’s exposure to food marketing can catalyse government action, yet research describing parent concerns is limited for media other than television. We examined parents' perceptions of UFM and their views on potential policies to address UFM in supermarkets and on digital devices – two settings where children are highly exposed to UFM and where little recent research exists. We conducted in-depth interviews with sixteen parents of children aged 7-12 from Victoria, Australia, analysing the data thematically. Parents perceived UFM as ubiquitous and viewed exposure as having an immediate but temporary impact on children’s food desires and pestering behaviours. Parents were concerned about UFM in supermarkets as they viewed it as leading their children to pester them to buy marketed products, undermining their efforts to instil healthy eating behaviours. Parents generally accepted UFM as an aspect of contemporary parenting. Concern for digital UFM was lower compared to supermarkets as it was not directly linked to pestering and parents had limited awareness of what their children saw online. Nevertheless, parents felt strongly that companies should not be allowed to target their children with UFM online and supported government intervention to protect their children. While parents supported government policy actions for healthier supermarket environments, their views towards restricting UFM in supermarkets varied as some parents felt it was their responsibility to mitigate supermarket marketing. These findings could be used to advocate for policy action in this area. Display omitted