Circular economy is an emerging concept that places an emphasis on strategies (e.g., reduce, reuse, recycle) to decouple resource use from economic growth, minimize waste and emissions, and maintain the highest utility along a product life cycle. The transition to a circular economy requires innovative solutions along entire value chains. This literature review was carried out to investigate the respective innovation systems that emerge along the wood-based and plastic-based value chains. To investigate different barriers to and drivers for the transition to a circular economy, the system functions of the technological innovation system framework were used. The results reveal that the two sectors hold different strategic positions and that barriers are dominant in the innovation system for plastics, while drivers are more prevalent in the innovation system for wood. This study is one of the first to direct a focus toward different industrial origins and their underlying logic, contributing to a better overall understanding of the circular economy.