The subject of this article by Katia Bertoldi, Vincenzo Vitelli, Johan Christensen and Martin van Hecke is Flexible Mechanical Metamaterials. Mechanical metamaterials exhibit properties and functionalities that cannot be realized in conventional materials. Originally the field focused on achieving unusual (zero or negative) values for familiar mechanical parameters, such as such as density, Poisson ratio or compressibility, but more recently new classes of metamaterials — including shape-morphing, topological and nonlinear metamaterials — have emerged.

These materials exhibit exotic functionalities, such as pattern and shape transformations in response to mechanical forces, unidirectional guiding of motion and waves, and reprogrammable stiffness or dissipation. In this Review, authors identify the design principles leading to these properties, discussing in particular linear and mechanism-based metamaterials (such as origami- and kirigami-based metamaterials), metamaterials harnessing instabilities and frustration and topological metamaterials. They conclude by outlining the future challenges for the design, creation and conceptualization of advanced mechanical metamaterials.