Dynamic bonds are a unique class of chemical bonds that can break and reform under specific conditions, giving polymers adaptable and reversible properties. These dynamic bonds can be classified into two main types: dynamic noncovalent bonds and dynamic covalent bonds. Unlike traditional covalent bonds, which are permanently fixed, dynamic bonds allow for structural reorganization, enabling materials to heal, reshape, or recover from stress. These properties make dynamic bonds highly valuable for applications in self-healing materials, recyclable polymers, biomedical devices, and soft robotics. Ionic bonds, a type of dynamic noncovalent bond formed through electrostatic interactions between oppositely charged ions, have been shown to create tough and resilient elastomers. This dissertation begins with a constitutive model framework to describe the response of elastomers with both ionic bonds and entanglements. The micromechanical model couples together chain stretching, ionic bond slipping, and entanglement evolution. The ionic bonds provide toughness by enabling plastic deformation in comparison to covalently crosslinked material and add strength compared to a linear polymer. Evolution of the entanglement density is taken as a key mechanism that can govern stiffness, toughness, and self-recovery in elastomers. The model is used to match bulk polyelectrolyte with different fractions of ionic components under a variety of loading histories. The model can help to design better material with high stiffness and toughness. Subsequently, the dissertation proposes using vitrimers with dynamic covalent bonds as composite resins that undergo thermally activated bond exchange reactions (BERs) to alleviate residual stress in polymer composites. Fiber Bragg grating measurements were conducted for a single glass fiber within bulk vitrimer that show the fiber strain in vitrimers with 5% catalyst is significantly lower than in those with 0% catalyst (minimal BERs expected) during both the curing and post-curing phases. A finite deformation, micromechanically-inspired model that integrates curing, thermal processes, and bond exchange reactions was developed, and implemented within a finite element model to simulate stress evolution within single fiber composite systems. The combination of experimental and computational results reveals that BERs can effectively mitigate the residual stress in the polymer matrix fiber composites.