Natural and synthetic rubbers (networks of polymer chains connected by irreversible chemical cross-links) cannot be repaired after damage, while discarded rubbers cannot be economically recycled and reprocessed. To avoid this shortcoming, a number of elastomers with dynamic covalent bonds have recently been synthesized that demonstrate recyclability, malleability and capability of autonomous self-healing due to thermally triggered bond-exchange reactions. A constitutive model is developed for the thermo-viscoelastic and thermo-viscoplastic responses of elastomers whose chains are bridged by adaptive bonds with the associative mechanism of rearrangement. Material parameters in the governing equations are determined by fitting observations in tensile tests, cyclic tests, relaxation tests and creep tests in a wide range of temperatures on covalently cross-linked rubber, thermoplastic elastomer, several elastomers and elastomer nanocomposites with dynamic covalent bonds, and epoxy vitrimers. Characteristic features are discussed of the thermo-mechanical behavior of elastomers with dynamic bonds and structure–property relations are established for these materials.