The concern for the environment and sustainability has intensified the search for alternative materials to replace non-degradable plastics. Poly(butylene adipate-co-terephthalate) (PBAT) is a bioplastic that has been extensively studied due to its excellent mechanical properties, which are similar to those of low-density poly(ethylene) (LDPE). However, the high cost of this polymer still hinders its wider application. Among the different approaches that have been studied, blending PBAT with thermoplastic starch (TPS) could be an interesting solution to reduce the cost of the material and increase the degradability of the blends. This review covers most of the work reported in recent years on PBAT/TPS blends, including the effects of starch plasticizers, starch modifications, processing methods, use of chain extenders, various compatibilizers, and additives used for different applications.