Among biomaterials, 3D networks with capacities to absorb and retain large quantities of water (hydrogels) or withstand significant deformation and stress while recovering their initial structures at rest (elastomers) are largely used in biomedical applications. However, when damaged, they cannot recover their initial structures and properties. To overcome this limitation and satisfy the requirements of the biomedical field, self-healable hydrogels and elastomers designed using (bio)degradable or bioeliminable polymer chains have been developed and are becoming increasingly popular. This review presents the latest advances in the field of self-healing degradable/bioeliminable networks designed for use in health applications. The strategies used to develop such networks based on reversible covalent or physical cross-linking or their combination via dual/multi-cross-linking approaches are analyzed in detail. The key parameters of these hydrogels and elastomers, such as mechanical properties, repair and degradation times, and healing efficiencies, are critically considered in terms of their suitabilities in biomedical applications. Finally, their current and prospective uses as biomaterials in the fields of tissue engineering, drug/cell delivery, and medical devices are presented, followed by the remaining challenges faced to ensure the further success of degradable self-healable networks.