Protective helmets

Embodiments of a protective helmet have a cushioning outer multilayer structure with at least two cushioning layers of materials having different densities and different geometric layouts, a multilayer hard inner structure attached to the interior surface of the cushioning multilayer structure, and an innermost cushioning structure attached to the inner surface of the multilayer hard inner structure. The multilayer hard inner structure is formed from at least two spaced layers of hard material and a layer of cushioning material therebetween. The innermost cushioning structure may be a multilayer structure similar to the outer multilayer structure with at least two cushioning layers of materials having different densities and different geometric layouts. The innermost cushioning structure may include sensors, optionally in a separate layer, and a thermal-control layer. A flexible thin cover extending around an outer surface of said shell and with or without graphics may be provided.