Fumaric polymers are macromolecules obtained from 1,2-disubstituted monomers, which provide special structural characteristics and therefore attractive physicochemical properties for their applications. Thus, in the present review, different radical polymerization mechanisms (conventional or living) are detailed and their characteristic kinetic parameters are shown. For example, the use of the initiator 2,2′-azobis(isobutyrate) (MAIB) allows to obtain polymers of higher molecular weight since it generates more stable primary radicals than those achieved with other azo initiators. The emergence of different controlled radical polymerization methodologies has resulted in the generation of new fumaric homo and copolymers with different properties. The structural characteristics of these materials analyzed by spectroscopic techniques and their relationship with properties in solutions, glass transition temperature, thermal stability and mechanical behavior are detailed in the present work. Finally, several biomedical and energy applications are described in which copolymers from fumaric and acrylic monomers were employed, combined or not with natural polymers to be used as scaffolds in the regeneration of bone and cartilage tissue, drug delivery systems, as flow or asphalt modifiers. From the complete reading of this review, it will be possible to achieve a global vision starting from the synthesis to the application of fumaric polymers in which the need of scaling this type of productions to reach specific industrial applications is visualized.