Medical adhesives that are strong, easy to apply and biocompatible are promising alternatives to sutures and staples in a large variety of surgical and clinical procedures. Despite progress in the development and regulatory approval of adhesives for use in the clinic, adhesion to wet tissue remains challenging. Marine organisms have evolved a diverse set of highly effective wet adhesive approaches that have inspired the design of new medical adhesives. Here we provide an overview of selected marine animals and their chemical and physical adhesion strategies, the state of clinical translation of adhesives inspired by these organisms, and target applications where marine-inspired adhesives can have a significant impact. We will focus on medical adhesive polymers inspired by mussels, sandcastle worms, and cephalopods, emphasize the history of bioinspired medical adhesives from the peer reviewed and patent literature, and explore future directions including overlooked sources of bioinspiration and materials that exploit multiple bioinspired strategies.