Mussel adhesive proteins (MAPs) have a unique ability to firmly adhere to different surfaces in aqueous environments via the special amino acid, 3,4-dihydroxyphenylalanine (DOPA). The catechol groups in DOPA are a key group for adhesive proteins, which is highly informative for the biomedical domain. By simulating MAPs, medical products can be developed for tissue adhesion, drug delivery, and wound healing. Hydrogel is a common formulation that is highly adaptable to numerous medical applications. Based on a discussion of the adhesion mechanism of MAPs, this paper reviews the formation and adhesion mechanism of catechol-functionalized hydrogels, types of hydrogels and main factors affecting adhesion, and medical applications of hydrogels, and future the development of catechol-functionalized hydrogels.