For some time, we and others have advanced a theory that soft materials—elastomers, gels, and living tissues—attain high toughness through inelasticity, just like metals. This theory has led to a worldwide search for mechanisms of inelasticity—sacrificial bonds that dissipate energy. The materials so created increase toughness by orders of magnitude, but suffer from a molecular disease: fatigue. Symptoms include excessive hysteresis and growth of cracks under cyclic stretch. They are unfit for applications such as artificial heart valves and soft robots. Recently, we have developed soft materials called elastic dissipaters. They have high toughness and low hysteresis. They are fatigue-resistant. This talk describes these materials, along with advances in adhesion of soft materials. Soft materials enable strong adhesion through topological entanglement.