The limits to linear models of production based on material extraction, manufacture, use, and disposal are becoming increasingly apparent across the global economy. The Circular Economy (CE) describes an alternative to this problematic "take-make-waste " linear model that is concerned with resource efficiency and waste minimization. The construction and demolition sector represents an important focus for a CE transition due to its significant environmental impact. The use of thermal insulation to reduce energy demand associated with heating and cooling in buildings is vital for reducing the sector's high environmental impact; however, there are significant challenges to recycling thermal insulation materials (IM). This study examines these challenges in the context of Switzerland and evaluates the potential for more circular management of expanded polystyrene and stonewool IM. The research provides an original analysis of the Swiss IM value chain in the context of the CE agenda based on a literature review, semi-structured interviews, and a workshop. Research gaps are highlighted based on scientific literature. The roles and agency of actors involved in the Swiss IM value chain are examined. Enablers of and barriers to wider IM recycling as reported by workshop participants are outlined. Interventions for tackling the current challenges faced for the recycling of thermal IM are suggested. Finally, an agenda for future research is proposed. Throughout the discussion, the importance of the involvement, commitment, and collaboration of stakeholders across the entire IM value chain for an effective and expedient transition to a CE is highlighted.