Biopolymers are natural polymers sourced from plants and animals, which include a variety of polysaccharides and polypeptides. The inclusion of biopolymers into biomedical hydrogels is of great interest because of their inherent biochemical and biophysical properties, such as cellular adhesion, degradation, and viscoelasticity. The objective of this Review is to provide a detailed overview of the design and development of biopolymer hydrogels for biomedical applications, with an emphasis on biopolymer chemical modifications and cross-linking methods. First, the fundamentals of biopolymers and chemical conjugation methods to introduce cross-linking groups are described. Cross-linking methods to form biopolymer networks are then discussed in detail, including (i) covalent cross-linking (e.g., free radical chain polymerization, click cross-linking, cross-linking due to oxidation of phenolic groups), (ii) dynamic covalent cross-linking (e.g., Schiff base formation, disulfide formation, reversible Diels-Alder reactions), and (iii) physical cross-linking (e.g., guest-host interactions, hydrogen bonding, metal-ligand coordination, grafted biopolymers). Finally, recent advances in the use of chemically modified biopolymer hydrogels for the biofabrication of tissue scaffolds, therapeutic delivery, tissue adhesives and sealants, as well as the formation of interpenetrating network biopolymer hydrogels, are highlighted.