This chapter explores narratives of innovation that address the challenges faced in the construction sector and associated firms in meeting climate change targets. Innovation is important to meet the targets, and there is an urgency reflected within continuously developing global strategies and policy initiatives. The chapter focuses on the interaction process between climate change targets at the policy level and the action/reaction of the construction sector firms, both owners/clients and suppliers/main contractors. It explores the way narratives of innovation are continuously promoted in textual forms – in Norway with the focus on working towards ‘zero emissions’ and in the UK with the focus on ‘low carbon’. Policy initiatives support innovation solutions support Norway’s climate change goals through a strong economic narrative. The chapter provides an outline of the narrative interactions between documented policy narratives and building industry firm narratives.