In recent years, there has been an increasing interest in shape-changing smart materials in design fields. The ability to design responsive architectures that adapt to different climatic conditions is, without doubt, an appealing idea. One area in which shape-changing materials are applied is in the design of building skins or envelopes. This paper presents a systematic review of the literature on the use of shape-changing materials in the development of active skin systems, identifying patterns in design and manufacturing strategies. We also note the stage of development of the proposed designs and whether performance analysis was conducted to predict their behaviour. The results show that the most commonly used materials are SMA (Shape Memory Alloys) and wood-based bio-composites. Other shape-changing materials used for developing skin systems are, in order of popularity, thermo bimetals, electroactive polymers, composite bimetals, shape memory polymers, and hydrogels. The patterns identified among the studies are (1) design strategies: smart material as the skin, smart material as the actuator, combination with other non-responsive materials, responsive structures, geometric amplification; and (2) manufacturing strategies: bilayer systems and additive manufacturing. Finally, while the argument for the development of responsive skin systems is often based on the idea of efficiency and improved performance, we found that few studies can predict the performance of such skin systems.