The term tensegrity, derived from tensional integrity, refers to a certain class of structural systems composed of bars and strings. Through adequate pre-stressing of their string members, tensegrity structures generally become mechanically stable. Traditional approaches for modeling their behavior assume that (i) bars are perfectly rigid, (ii) cables are linear elastic, and (iii) bars experience pure compression and strings pure tension. In addition, a common design constraint is to assume that the structure would fail whenever any of its bars reaches the corresponding Euler buckling load. In reality, these assumptions tend to break down in the presence of dynamic events. In the first part of this talk, we will introduce a physics-based reduced-order model to study aspects related to the dynamic and nonlinear response of tensegrity-based planetary landers. We will then adopt our model to show how, under dynamic events, buckling of individual members of a tensegrity structure does not necessarily imply structural failure, thus significantly expanding the design space for such vehicles. In the second part of this talk, we will show how lessons learned from our tensegrity planetary lander can be translated into to the development novel metamaterials. We will introduce the first known class-two 3D tensegrity metamaterial, and show that this new topology exhibits unprecedented static and dynamic mechanical properties.