Vitrimers are a new class of cross-linked materials that are capable of network topology alternation through the associative dynamic bond-exchange mechanism, which has recently been invented to solve the problem of conventional cross-linked materials, such as poor recyclability and healability. Thus far, the concept of vitrimers has been applied to various commercial polymers, e.g., polyesters, polylactides, polycarbonates, polydimethylsiloxanes, polydienes, polyurethanes, polyolefins, poly(meth)acrylates, and polystyrenes, by utilizing different compatible bond-exchange reactions. In this review article, the concept of vitrimers is described by clarifying the difference from thermoplastics and supramolecular systems; in addition, the term “associative bond-exchange” in vitrimers is explained by comparison with the “dissociative” term. Several useful functions attained by the vitrimer concept (including recyclability and healability) are demonstrated, and recent molecular designs of vitrimers are classified into groups depending on the types of molecular frameworks. This review specifically focuses on the vitrimer molecular designs with commercial polymer-based frameworks, which provide useful hints for the practical application of the vitrimer concept.