•Key mechanics were reviewed for stretchable batteries and supercapacitors by structural designs.•Four representative strategies of structural designs were discussed.•Design concepts, mechanical behaviors, and analytical/computational models were reviewed.•Perspectives were provided on the remaining challenges and opportunities for future research. The last decade has witnessed fast developments and substantial achievements that have been shaping the field of stretchable electronics. Due to a persistent need of equally stretchable power sources, especially for some emerging bio-integrated applications enabled by this unusual class of electronics, stretchable energy storage systems have been attracting increasing attentions in the past few years. This article reviews the mechanics of stretchable batteries and supercapacitors that are enabled by novel structural designs of hard and soft components, involving four representative strategies (i.e., wavy, wrinkled design, origami design, serpentine bridge-island design, and fractal inspired bridge-island design). The key mechanics of each strategy is summarized, with focuses on the design concepts, unique mechanical behaviors, and analytical/computational models that guide the design optimization. Finally, some perspectives are provided on the remaining challenges and opportunities for future research.