Mechanism-based mechanical metamaterials are designer materials that experience microscale buckling in response to mechanical deformation. A rapidly-growing literature is emerging concerning the design and use of such materials. Their analysis challenges our understanding of the relationship between microscopic and macroscopic behavior in geometrically nonlinear mechanical systems. After a broad introduction to the area, this talk will focus especially on a particular example: the Kagome metamaterial. A key issue is whether its macroscopic behavior is adequately modeled by elastic energy minimization (even though its energy landscape is very nonconvex, with many local minima). I?ll discuss theoretical work with Xuenan Li, which has determined the consequences of this model; and I?ll discuss ongoing numerical work with Katia Bertoldi, Bolei Deng, and Xuenan Li, which is exploring the adequacy of the model.