Shape memory polymers (SMPs) have the capacity of memorizing a temporary shape and recovering their initial shape in response to various external stimuli. As one of promising class of intelligent materials, it has attracted great attention because of its potential applications in many areas, such as biomaterials and biotechnology, automotive industry, and aerospace field. Aliphatic polymers play an important role in the molecular design of SMPs owing to its excellent biodegradability and biocompatibility, and suitable thermal transition temperature range. This review focuses on the recent progress of shape memory polymers based on the aliphatic polyesters such as poly(lactic acid) (PLA), poly ( p -dioxanone) (PPDO), poly(butylene succinate) (PBS), poly( ω -pentadecalactone) (PPDL) and poly( ɛ -caprolactone) (PCL) and so on. From the view of architecture design, different systems are classified by block copolymers, crosslinking networks and interpenetrating networks. The influence of architectural features on the shape memory behaviors is also discussed. The block copolymers have been identified a typical mature system in design of dual-shape material, and the crystalline aliphatic polyesters can be served as the netpiont or the molecular switch in a SMP, depending on its transition temperature range among the binary systems. The thermoplastic feature of block copolymers endows an easy processibility. The various architectures of crosslinking network meet the increasing demand of SMPs design. Constructing network with crystallizable polyester segment such as PCL may achieve SMPs in one-way and two-way mode, and the stress-free two-way mode can also be realized by an elaborate architecture with pre-programed treatment. Embedding two segments in one network may achieve a triple-shape memory effect, meanwhile, incorporating two segments in an interpenetrating polymer network may result in a triple-shape material with improved performance. Recently, the SMPs based on dynamic networks become the new trend, which may combine the self-healing with shape memory effect in one system, and both dynamic covalent bond and non-covalent bond have been concerned. In order to fulfill the increasing requirement of application, the SMPs with multi-shape memory effect, multi-responsibility and multi-functionality are highly expected.