With the growing potential of the Internet of Things, displays are being utilized to provide various types of information in every aspect of daily life, leading to the expansion of form-factor-free displays. Stretchable displays are considered the ultimate goal in form factor innovation, and they are not limited to rectangular shapes with deformation characteristics suited to target applications. Because reliable stretchable displays should be robust under uniaxial and biaxial strain, there have been efforts to tailor mechanical stress with promising strategies from structural and material perspectives. This review focuses on strain-engineering stretchable substrates for free-form display applications. First, we introduce deformable substrates with structural stretchability, achieved by incorporating buckling and Kirigami structures into plastic films, and we systematically analyze the tensile deformation characteristics based on design elements. In addition, we examined intrinsically stretchable elastomeric substrates, which have gained considerable attention due to recent advances in material and processing technologies. Their spatial modulus patterning is studied by applying optimized design principles, achieved through network alignment and crosslinking control in homogeneous elastomers, as well as by incorporating heterogeneous structures within the elastomer materials. Finally, we discussed state-of-the-art stretchable display applications employing strain-engineered stretchable substrates, focusing on advantageous materials and structures based on the display components, processes, and target deformation characteristics. Building on this foundation, we discuss the development of next-generation free-form displays and aim to contribute to their application in various static and dynamic deformation environments.
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