Turning thermosets into fully sustainable materials requires utilization of biobased raw materials and design for easy recyclability. Here, dynamic covalent chemistry for fabrication of covalent adaptable networks (CANs) could be an enabling tool. CAN thermosets ideally combine the positive material properties of thermosets with thermal recyclability of linear thermoplastics. Among the dynamic covalent bonds, imine bond, also called Schiff base, can participate in both dissociative and associative pathways. This induces potential for chemical recyclability, thermal reprocessability and self-healing. This review presents an overview of the current research front of biobased thermosets fabricated by Schiff base chemistry. The discussed materials are categorized on the basis of the employed biobased components. The chemical approaches for the synthesis and curing of the resins, as well as the resulting properties and recyclability of the obtained thermosets are described and discussed. Finally, challenges and future perspectives are briefly summarized.