Most materials obtain their mechanical properties from the atoms and molecules they are made of. Mechanical metamaterials are different: they derive their properties from the shape of their building blocks and can be made from a variety of base materials. In many dynamical responses, dissipation plays a key role. However, although the effect of the constitutive materials’ dissipation on mechanical instabilities has been well studied, the role of dissipation in the extreme mechanics of mechanical metamaterials remains poorly understood. One can therefore ask the question: How can viscoelasticity enhance the functionality of mechanical metamaterials? This is the question we have tried to answer in this thesis. More specifically, in this thesis we have provided a new set of tools and methods which can be used to enhance the functionality of mechanical metamaterials, with and without viscoelasticity. First, we demonstrate that dissipation can delay buckling instabilities, which we use to generate both extreme shock and vibration damping in mechanical metamaterials, without mass or stiffness penalty. Then, we introduce a novel class of mechanical metamaterials, which we name oligomodal metamaterials, that offer a constant number of modes larger than one regardless of system size. We then harness viscoelasticity with these oligomodal metamaterials to generate multi-functionality. Finally, we show that we can also inversely design such oligomodal metamaterials using a novel sequential nonlinear method. With so many possibilities to harness dissipation in the design of mechanical metamaterials, we anticipate applications in a variety of cases, including aerospace, sensitive instruments and soft robotics.