Thermosets are known to be very reliable polymeric materials for high-performance and light-weight applications, due to their retained dimensional stability, chemical inertia and rigidity over a broad range of temperatures. However, once fully cured, they cannot be easily reshaped or reprocessed, thus leaving still unsolved the issues of recycling and the lack of technological flexibility. Vitrimers, introduced by Leibler et al. in 2011, are a valiant step in the direction of bridging the chasm between thermoplastics and thermosets. Owing to their dynamic covalent networks, they can retain mechanical stability and solvent resistance, but can also flow on demand upon heating. More generally, the family of Covalent Adaptable Networks (CANs) is gleaming with astounding potential, thanks to the huge variety of chemistries that may enable bond exchange. Arising from this signature feature, intriguing properties such as self-healing, recyclability and weldability may expand the horizons for thermosets in terms of improved life-span, sustainability and overall enhanced functionality and versatility. In this review, we present a comprehensive overview of the most promising studies featuring CANs and vitrimers specifically, with particular regard for their industrial applications. Investigations into composites and sustainable vitrimers from epoxy-based and elastomeric networks are covered in detail.