Polymeric vascular bioresorbable stents (BRSs) have been widely used for the treatment of coronary artery diseases. While additive manufacturing (AM) is changing the landscape of the healthcare sector by enabling the realization of patient‐specific stents with highly complex structures. There are, however, challenges associated with the use of polymeric BRS, particularly in‐stent restenosis (ISR), related to its poor mechanical properties. Therefore, the aim of this review is to provide an overview of recent advancements in the development of polymeric BRSs designed to meet both mechanical and biological requirements. First, biopolymers as well as shape memory polymers (SMPs) that are suitable for BRSs are highlighted and briefly described. Second, different types of designing structures of vascular stents in addition to introducing effective mechanical metamaterials, e.g., negative Poisson ratio (NPR) structures are addressed. Subsequently, AM methods currently being used to fabricate polymeric BRSs, are discussed and compared with conventional fabrication methods. Lastly, future directions for research are proposed in relation to existing challenges to the realization of a new generation of AM BRSs. Overall, this paper serves as a benchmark for future cardiovascular applications, especially in order to obtain clinically viable polymeric vascular stents by selecting suitable polymers, designs, and AM technologies.