Mechanical metamaterials are synthetic materials that exhibit microscale buckling in response to mechanical deformation. These artificial structures resemble elastic composites but can be even more degenerate, as they may deform with almost zero elastic energy. We refer to such deformations with very small elastic energy as mechanisms. In this talk, I will focus on a particularly rich example: the Kagome metamaterial, which exhibits many mechanisms that, at first glance, seem incompatible with having a meaningful macroscopic energy. I will present our model of the Kagome metamaterial, which yields a well-defined effective energy and allows us to analyze its large-scale elastic behavior. Our macroscopic theory reveals that compressive conformal maps are the only deformations that achieve zero effective energy. If time permits, I will transition from the static viewpoint to a dynamic one and discuss how slowly varying deformations can influence wave propagation in these soft mechanical metamaterials. The first part, focusing on the static perspective, is a joint work with Robert V. Kohn, while the second part, on the dynamic perspective, is a joint work with Michael I. Weinstein.