Hydrogels are attractive biomaterials with favorable characteristics due to their water uptake capacity. However, hydrogel properties are determined by the cross-linking degree and nature, the tacticity, and the crystallinity of the polymer. These biomaterials can be sorted out according to the internal structure and by their response to external factors. In this case, the internal interaction can be reversible when the internal chains are led by physicochemical interactions. These physical hydrogels can be synthesized through several techniques such as crystallization, amphiphilic copolymers, charge interactions, hydrogen bonds, stereo-complexing, and protein interactions. In contrast, the internal interaction can be irreversible through covalent cross-linking. Synthesized hydrogels by chemical interactions present a high cross-linking density and are employed using graft copolymerization, reactive functional groups, and enzymatic methods. Moreover, specific smart hydrogels have also been denoted by their external response, pH, temperature, electric, light, and enzyme. This review deeply details the type of hydrogel, either the internal structure or the external response. Furthermore, we detail some of the main applications of these hydrogels in the biomedicine field, such as drug delivery systems, scaffolds for tissue engineering, actuators, biosensors, and many other applications.