Shape memory polymers (SMPs) are capable of memorizing one or more temporary shapes and recovering to the permanent shape upon an external stimulus that is usually heat. Biodegradable polymers are an emerging family within the SMPs. This minireview delivers an overlook on actual concepts of molecular and supramolecular architectures which are followed to tailor the shape memory (SM) properties of biodegradable polyesters. Because the underlying switching mechanisms of SM actions is either related to the glass transition (Tg) or melting temperatures (Tm), the related SMPs are classified as Tg- or Tm-activated ones. For fixing of the permanent shape various physical and chemical networks serve, which were also introduced and discussed. Beside of the structure developments in one-way, also those in two-way SM polyesters were considered. Adjustment of the switching temperature to that of the human body, acceleration of the shape recovery, enhancement of the recovery stress, controlled degradation, and recycling aspects were concluded as main targets for the future development of SM systems with biodegradable polyesters.