Building envelopes are primarily responsible for buildings' energy consumption and environmental performance. Kinetic building shadings have emerged as an alternative for improved environmental performance in the past years, dynamically adjusting to changing outdoor conditions. Elastic kinetic systems rely on the flexible nature of their components to achieve motion and can be used in kinetic building shades. Unlike their rigid counterparts, these mechanisms can reduce the part count in kinetic systems (and, thereby, their mechanical complexity) and potentially adapt to synclastic and anticlastic surfaces. This manuscript reviews elastic kinetic systems used in building envelope design, that is, building envelope systems that rely on materials’ elastic properties to their advantage to achieve motion. The first section of the review includes an overview of biomimetics for kinetic building envelope design drawing parallels between plant kinematics and elastic kinetics in regard to material strategies and actuation. The second section of the review analyzes thirteen case studies regarding the level of development, materials used, and actuation strategies. The study showed that polymer-based composites are mainly used to construct elastic kinetics and that other low-carbon materials could be explored in future research. From the case study analysis, a taxonomy was developed to classify their actuation strategies (manual, pneumatic or mechanical, actuation with smart materials) and elastic mechanisms (linear and surface elements which can be compliant or bistable). An area for future work might consider abstracting actuation mechanisms from fast motile plants to offer insights for combining passive actuators with multi-stable elastic kinetics for fast adaptation in kinetic building envelopes.