Innovative materials and systems for flexible and lightweight energy-efficient solutions in construction can help achieve the objective of more efficient buildings. This literature review categorizes these solutions into three categories: materials/systems topology, design flexibility from 3D-printing technologies, and innovative solutions for building envelope designs. The review shows a significant increase in interest in this research topic in recent years, with an average annual growth rate of about 73%, with most research focused on the design and thermal aspects, as well as the material typology and 3D-printing technologies. According to the review, flexible and lightweight systems can be applied to all building sectors, and retrofitting existing buildings may become the primary approach. However, there is no specific European regulation for these systems, and a more holistic design approach is needed, involving both designers/constructors and users, to plan for actual social, economic, and environmental impacts.