Mussels are well-known for their extraordinary capacity to adhere onto different surfaces in various hydrophillic conditions. Their unique adhesion ability under water or in wet conditions has generated considerable interest towards developing mussel inspired polymeric systems that can mimic the chemical mechanisms used by mussels for their adhesive properties. Catechols like 3,4-dihydroxy phenylalanine (DOPA) and their biochemical interactions have been largely implicated in mussels' strong adhesion to various substrates and have been the centerpoint of research and development efforts towards creating superior tissue adhesives for surgical and tissue engineering applications. In this article, we review bioadhesion and adhesives from an engineering standpoint, specifically the requirements of a good tissue glue, the relevance that DOPA and other catechols have in tissue adhesion, current trends in mussel-inspired bioadhesives, strategies to develop mussel-inspired tissue glues, and perspectives for future development of these materials.