Following current trends toward development of novel materials and structures, this volume explores the concept of high-performance metamaterials and metastructures with extremal mechanical properties, inspired by tensegrity systems. The idea of extremal materials is applied here to cellular tensegrity lattices of various scales. Tensegrity systems have numerous advantages: they are lightweight, have a high stiffness-to-mass ratio, are prone to structural control, can be applied in smart and adaptive systems, and exhibit unusual mechanical properties. This study is focused on tensegrity lattices, whose inner architecture resembles that of cellular metamaterials, but which are aimed at civil engineering applications in non-material scales. It proposes a methodology for investigation of extremal mechanical properties of such systems, based on discrete and continuum approaches, including the discussion on scale effects. It proves that, similarly to tensegrity-based metamaterials, tensegrity metastructures are able to exhibit extremal mechanical behaviour. This book is directed to researchers and scientists working on metamaterials and tensegrity systems, developing energy-absorption solutions for building and transport industry. The findings described in this monograph can also be useful in other fields of applied sciences, such as civil engineering, robotics and material science.