Liquid crystal elastomers (LCEs) have recently been described as a new class of matter. Here we review the evidence for the novel conclusion that the fibrillar collagens and the dragline silks of orb web spiders belong to this remarkable class of materials. Unlike conventional rubbers, LCEs are ordered, rather than disordered, at rest. The identification of these biopolymers as LCEs may have a predictive value. It may explain how collagens and spider dragline silks are assembled. It may provide a detailed explanation for their mechanical properties, accounting for the variation between different members of the collagen family and between the draglines in different spider species. It may provide a basis for the design of biomimetic collagen and dragline silk analogues by genetic engineering, peptide- or classical polymer synthesis. Biological LCEs may exhibit a range of exotic properties already identified in other members of this remarkable class of materials. In this paper, the possibility that other transversely banded fibrillar proteins are also LCEs is discussed.