Hydrogels have been developed for different biomedical applications such as in vitro culture platforms, drug delivery, bioprinting and tissue engineering. Enzymatic cross-linking has many advantages for its ability to form gels in situ while being injected into tissue, which facilitates minimally invasive surgery and adaptation to the shape of the defect. It is a highly biocompatible form of cross-linking, which permits the harmless encapsulation of cytokines and cells in contrast to chemically or photochemically induced cross-linking processes. The enzymatic cross-linking of synthetic and biogenic polymers also opens up their application as bioinks for engineering tissue and tumor models. This review first provides a general overview of the different cross-linking mechanisms, followed by a detailed survey of the enzymatic cross-linking mechanism applied to both natural and synthetic hydrogels. A detailed analysis of their specifications for bioprinting and tissue engineering applications is also included.