Vitrimers are permanent yet dynamic polymer networks that ideally behave like conventional thermosets at service temperatures but flow like vitreous glasses at processing temperatures. They are characterized by constant, temperature‐independent network connectivity as well as the ability to completely relax stress as a result of dynamic exchange reactions between the cross‐links. Other important features include enhanced insolubility, healing properties, and facile shaping. Since the introduction of vitrimers in 2011, which were epoxy‐acid and epoxy‐anhydride resins loaded with a transesterification catalyst, many kinds of dynamic covalent chemistries have been employed in polymer networks to create new vitrimers. Born from these advancements, exciting new applications have been reported that cannot be realized with conventional thermosets. In this article, we introduce fundamental principles of vitrimer science and provide an overview of recent advances in vitrimer chemistry. Finally, we discuss the use of vitrimers in recycling, shape‐memory materials, composites, and a variety of other nascent applications.