Recent developments in material design have seen an exponential increase of polymers and polymer composites that can repair themselves in response to damage. In this review, a distinction is made between extrinsic materials, where the self-healing property is obtained by adding healing agents to the material to be repaired, and intrinsic materials, where self-healing is achieved by the material itself through its chemical nature. An overview of the crosslinking chemistries used in self-healing materials will be given, discussing the advantages and drawbacks of each system. The review is not only aiming to enable researchers to compare their ongoing research with the state-of-the-art but also to serve as a guide for the newcomers, which allows for a selection of the most promising self-healing chemistries.