Many creatures use adhesive polymers and structures to attach to inert substrates, to each other, or to other organisms. This is the first major review that brings together research on many of the well-known biological adhesives dealing with bacteria, fungi, algae, and marine and terrestrial animals. As we learn more about their molecular and mechanical properties we begin to understand why they adhere so well and with this comes broad applications in areas such as medicine, dentistry, and biotechnology.