Phil Messersmith at Northwestern is a leader in the field of bio-inspired adhesives (http://faculty.mccormick.northwestern.edu/phillip-messersmith/). His work on developing DOPA-modified adhesives derived from mussels has been feature in Nature and PBS News Hour.
Several surgical glues are FDA-approved including fibrin glue (Tisseal) and urethane-based adhesives (TissuGlu). Furthermore, synthetic polymers like paloxamer and aldehyde-functionalized poly(ethylene glycol)-poly(glycolic acid-lactic acid) copolymers have been used for tissue adhesion in preclinical studies.