Bioinspiration - using insights into the function of biological systems for the development of new engineering concepts - is already a successful and rapidly growing field. However, only a small portion of the world's biodiversity has thus far been considered as a potential source for engineering inspiration. This means that vast numbers of biological systems of potentially high value to engineering have likely gone unnoticed. Even more important, insights into form and function that reside in the evolutionary relationships across the tree of life have not yet received attention by engineers. These insights could soon become accessible through recent developments in disparate areas of research; in particular, advancements in digitization of museum specimens, methods to describe and analyze complex biological shapes, quantitative prediction of biological function from form, and analysis of large digital data sets. Taken together, these emerging capabilities should make it possible to mine the world's known biodiversity as a natural resource for knowledge relevant to engineering. This transformation of bioinspiration would be very timely in the development of engineering, because it could yield exactly the kind of insights that are needed to make technology more autonomous, adaptive, and capable of operation in complex environments.