Advancements in science and technology, particularly in ultrashort-pulse lasers and refrigeration, have highlighted the wave-like behavior of heat propagation. Consequently, the generalized theory of thermoelasticity, which addresses finite-speed heat conduction, has gained widespread attention. Research indicates that materials with memory and path-dependent characteristics exhibit abnormal diffusion and anomalous heat conduction. However, the traditional generalized theory of thermoelasticity relies on integer-order differential terms in the heat conduction equation. These terms are based on the definition of local limits and only consider the current state of a material point, failing to account for memory-dependent characteristics. In contrast, fractional calculus uses convolution integrals to define its concepts, analyzing differentiation and integration of any real order, as well as methods for solving differential equations containing derivatives of any real order. The integral terms in fractional calculus can describe memory-dependent processes of a system. This paper introduces the development of fractional-order generalized theory of thermoelasticity and fractional calculus, summarizing recent research in this area, including the effects of magneto-electric multi-field coupling, diffusion, and viscoelasticity on the response of fractional-order generalized thermoelastic problems, as well as fractional-order heat conduction in biological tissues. It also identifies limitations in current studies, such as the challenges of short time scales in experimental research and the lack of exploration into high-frequency and high-gradient electromagnetic fields on thermoelastic responses. By addressing these topics, the paper provides a comprehensive overview of the current state and emerging trends in fractional-order generalized thermoelastic problems, aiding researchers in advancing their investigations in this field.