Bioinspired supramolecular adhesives have been recently emerging as novel functional materials, which have shown a wide range of applications in wearable sensors and tissue engineering such as tissue adhesives and wound dressings. In this review, we summarize and discuss two main types of biologically inspired supramolecular adhesives from adhesive proteins and nucleic acids. The widely studied catechol-based adhesives, that originated from adhesive proteins of marine organisms such as mussels, and recently emerging nucleobase-containing supramolecular adhesives are both introduced and discussed. Both bioinspired adhesives from nucleic acids and adhesive proteins involve multiple supramolecular interactions such as hydrogen bonding, hydrophobic interactions, π-π stacking, and so on. Several major types of these bioinspired adhesives are summarized, respectively, including polymer-based, hydrogel-based, and other types of adhesives. The novel molecular design and adhesion properties are focused on and highlighted for each type of bioinspired adhesive. In addition, the potential applications of these bioinspired supramolecular adhesives in different realms including tissue engineering and biomedical devices are discussed. This review concludes with issues and challenges in the area of the bioinspired adhesives, hopefully promoting further developments and broader applications of novel supramolecular adhesives.