This chapter discusses extremal mechanical behavior of tensegrity-inspired metamaterials and structures. It focuses on the identification of extremal properties of modular lattices based on basic tensegrity cells. First, two approaches to the analysis of tensegrity lattices in various scales are described: discrete and continuum, with a special attention paid to the effect of scale when applying the concept of extremal materials to bigger structural systems. Then, two examples of tensegrity lattices are analyzed: a 2D lattice based on hexagonal modules and a 3D lattice based on expanded octahedron. Parameters leading to soft and stiff deformation modes are determined and equivalent mechanical properties, such as Young’s and shear moduli and Poisson’s ratios, are calculated.