This review is about the fundamentals and practical issues in applying both heating and solvent responsive shape memory polymers (SMPs) for implant biomedical devices via minimally invasive surgery. After revealing the general requirements in the design of biomedical devices based on SMPs and the fundamentals for the shape‐memory effect in SMPs, the underlying mechanisms, characterization methods, and several representative biomedical applications, including vascular stents, tissue scaffolds, occlusion devices, drug delivery systems, and the current R&D status of them, are discussed. The new opportunities arising from emerging technologies, such as 3D printing, and new materials, such as vitrimer, are also highlighted. Finally, the major challenge that limits the practical clinical applications of SMPs at present is addressed.