Shape memory polymers (SMPs) are smart materials that can alter their shape from a temporary shape to a permanent shape upon external stimuli. This unique property of SMP has shown enormous potential and breakthrough discoveries in biomedical engineering. A significant number of SMP based research publications in the recent past have demonstrated the researchers’ thirst to introduce SMP based devices to the biomedical fields. SMPs favour minimally invasive surgeries and showed enormous potential in vascular stents. However, SMP-based vascular stents have not been realised to date, indicating a lack of high-quality research outputs. Most studies either repeat or provide only minor extensions to ongoing research. This article reviews SMP materials used for vascular stent development and briefly introduces SMP, architecture, and history.Followed by SMP vascular stent fabrication methods, responsive physical behaviour, the performance of the vascular stents, limitations, and vitro and vivo clinical results. Finally, challenges and future directions of SMP vascular stents are identified and highlighted.