The attainment of both strength and toughness is a vital requirement for most structural materials; unfortunately these properties are generally mutually exclusive. Although the quest continues for stronger and harder materials, these have little to no use as bulk structural materials without appropriate fracture resistance. It is the lower-strength, and hence higher-toughness, materials that find use for most safety-critical applications where premature or, worse still, catastrophic fracture is unacceptable. For these reasons, the development of strong and tough (damage-tolerant) materials has traditionally been an exercise in compromise between hardness versus ductility. Drawing examples from metallic glasses, natural and biological materials, and structural and biomimetic ceramics, we examine some of the newer strategies in dealing with this conflict. Specifically, we focus on the interplay between the mechanisms that individually contribute to strength and toughness, noting that these phenomena can originate from very different lengthscales in a material's structural architecture. We show how these new and natural materials can defeat the conflict of strength versus toughness and achieve unprecedented levels of damage tolerance within their respective material classes.